As I understand the SC decision, it clarifies that impeachment by Congress is the only possible penalty for certain acts by the President in his or her official capacity.
Taken without context, a law or an article of a constitution which assigns certain crimes or perpetrators to certain courts is entirely normal. There are countries where soldiers get a court martial for 'civilian' crimes, countries where juveniles go to different courts than adults, countries where labor disputes are handled by different courts than other contract matters. One might question if it is a good idea to use a procedure which can only result in impeachment or non-impeachment for the President, but there are many countries where juvenile courts are restricted to less severe punishments than adult courts, too.
So the government would appear to be still constitutional. One might question if the result is a wise constitutional system, but even an unwise constitutional system allows constitutional government.