Short answer:
No. The only destructive thing thing about 5e is the continued inclusion of Bards and the Soulless, Dead-eyed Elves.
Long Answer:
No. This falls under "A rising tide lifts all ships." It has always been the case that D&D (and D&D variants, like PF) have been the 800 pound gorilla in the TTRPG market. Arguments can be made as to whether this is good or bad in terms of introducing players to the hobby. But the following two things are true:
1. There will always be some contingent of people that will continue to play D&D, say that D&D is all they need, etc.
2. There will always be a contingent of people that will grow dissatisfied with D&D over time, and will branch out to other games.
The massive success of 5e has brought all sorts of new players to the hobby. Some will fall away, but many will stay, and some of those many will be playing alternate games- players that would not have been in the hobby to begin with.
The success of D&D right now is providing a whole new generation of TTRPG players, many of them will end up playing other games as well. It's a good thing.
EDIT: Kinja'd by
@Fanaelialae !