tl;dr
It's most certainly a ternary rhythm, but, considering the possible overall meter of the piece and the convention for which compound rhythms are normally based on eighths, it's quite possible it is 3/8, not 3/4.
Insights
As a follow up to John's answer, if you have no way to get the source material or directly ask the composer, then you need to consider the possible "rhythm hierarchy" of the composition. Since the piece also contains some tempo variations, there will always be some level of inaccuracy, that also depends on how you may interpret the musical meaning of what you hear and how you decide its importance in your transcription.
Generally speaking, a composition normally has just one meter. In reality, many compositions have more than one, then you generally have specific meters for each relatively long section, or short passages with a different meter (possibly, even just one bar). Yet, you may decide that the "main reference meter" is not based on the maximum length of a section with a specific meter, but its importance.
This is not so different from knowing or deciding the key of a composition: consider the case of One Note Samba, which is traditionally in B flat, even though it fundamentally has just one bar using the chord of that key.
Still, when deciding the main key of a piece, we cannot just consider the percentage of notes in the melody or chords that are in the same key.
In general, the melody helps to find the key based on their rhythmic relevance (position in the bar, relation to the beats, duration), but that may not always be possible (consider the One Note Samba case above). A music piece also has a harmonic rhythm and its own hierarchy, which may help to define/confirm/contradict, to a certain accuracy, the possible meter of a piece.
Now, after listening to the piece, I think we can all agree that the basic rhythm references could be considered as eights and/or quarters. A general rhythm scheme and rhythmic relation can be recognized, and conventions tell us that, for instance, the first notes in the melody are probably eights and sixteenths, as much as the first two notes in the bass should be quarters.
Still, let's stop and consider the first two bars in that piece.
The very first bar is a bit ambiguous. If we only consider the melody, it's rhythmically straight forward, though:
![rhythm transcription of the melody in the first two bars](https://cdn.statically.io/img/i.sstatic.net/XWyVHIRc.png)
- it almost certainly has 8 eighths (or 4 quarters);
- it stops at the fifth eighth or the down beat of the third quarter;
- it "reprises" with an upbeat for the new bar and creates a similar rhythm in there, stopping again on the third beat (or fifth eighth);
- the harmonic accompaniment follows a similar approach;
What happens to the bass line, though? We should always consider that the rhythm of the lower/bass note is quite important to define the harmony and, to some level, the overall rhythm.
The first bar has the following:
![rhythm of the bass of the first bar](https://cdn.statically.io/img/i.sstatic.net/M623Lirp.png)
But considering that the third to last note is also the tonic of the chord in that point, are we sure that it shouldn't be written as such?
![alternate rhythm of the bass of the first bar](https://cdn.statically.io/img/i.sstatic.net/E4MBzLhZ.png)
In this case, it would be an 8/8 intended as 2+3+3. Attaching the melody:
![alternate rhythm for both parts](https://cdn.statically.io/img/i.sstatic.net/oI3eiEA4.png)
Still, as said above, one measure (even if it's the first) rarely dictate the overall meter.
Let's see what the bass does on the second measure:
![rhythm of the bass in the second bar](https://cdn.statically.io/img/i.sstatic.net/YFbjGBHx.png)
While it may be possible to still consider this as 2+3+3, the relevance of the sixteenths within the context makes them almost as similar to an ornament.
Up to this point, statistically speaking, we may safely believe that the piece is still in 4/4 and consider the odd rhythm/melodic accents of the first bar as peculiar of the piece: the rhythm is odd, not its meter.
The third bar can theoretically confirm this:
![possible rhythm of the third bar](https://cdn.statically.io/img/i.sstatic.net/pzgDEaqf.png)
Then, the fourth bar arrives. An educated guess would tell us that the meter has changed, based on the melody and the bass, as it's almost certainly a 12/8:
![probable rhythm of the fourth bar](https://cdn.statically.io/img/i.sstatic.net/9QTytCvK.png)
While, as said, a single bar doesn't decide the overall meter, it still may be an important hint, especially considering the ambiguity of the first bars.
The few following bars are most certainly based on 5 eighths (3+2), with semi phrases lasting two bars. The pattern is the following:
![rhythm and meter for bar five to eight](https://cdn.statically.io/img/i.sstatic.net/WitOgehw.png)
Then something changes. The third repetition of the pattern above slows down tempo a lot, but considering similar movements of the voices, we can assume that it still follows the same meter.
Then what? At circa 22 seconds from the beginning we have a further abrupt tempo change that is difficult to contextualize. Still, the melody has a similar pattern: the main note of the melody, followed by the note below and again the original one, both of smaller duration. Again the same, with the note above.
Since we're slowing down, another educated guess would tell us that the logical meter relation haven't changed: it's just slower, and it's 2/8.
After two bars of the above, we get back to 5/8 three times (with a slight rit. at the end of each bar).
And we're finally here, the point at hand. At circa 35 seconds we have something similar to the 5/8 above, but that fourth repetition takes another direction based on the second part/beat of that bar.
We clearly have a "3 beats" based section repeated four times, which could be transcribed as the following:
![possible transcription of the bars at point](https://cdn.statically.io/img/i.sstatic.net/9QiDzDHK.png)
Obviously, the above could be written as 2/8 + 12/8 (which we've already seen above), or even 14/8.
Still, the general pattern of the melody (possibly in relation with the accompaniment), which dictates the general reference meter or meters, tells us that this specific section of the piece is ternary, not binary.
Note, though, that this may not be absolutely true:
- this is an educated guess, based on the "statistics" of the piece (it ends just a few "bars" after that);
- if the piece actually continued with a more "binary" concept, it would have make sense to switch to that 6/8 somewhere in the bars above;
- the composer may have thought that the piece is fundamentally based on compound metre, but the performer may have chosen a rendition that doesn't follow it; that isn't impossible, but remember that:
- the performer may be wrong;
- the composer may be wrong, and realize, after listening to some renditions of their piece and discussing with performers, that they actually were really wrong; or not;
Final considerations
We have to remember that music notation is just a way to render an artistic and somehow personal idea. It's an arbitrary convention that tries to translate a completely different medium. Most of the times, a proper transcription is reliable. Some of them, though, it cannot be in the first place, and trying to fixate too much on some aspects is quite irrelevant.
If you're transcribing for your own good, you shouldn't care too much. Just write what you need, and leave the rest to your interpretation.
If you're doing it for others, consider various aspects, including:
- the target of those transcriptions (readability is sometimes more important than accuracy);
- the composer intent;
- the possible accepted convention, including common renditions, and how that may be important for your purposes;
- how the difference in writing may actually affect playing, both in reading and in rendition;