In my estimation, most likely not. Game companies make non-D&D games all the time, and if companies making non-D&D games had any real impact on D&D we wouldn't have seen D&D grow so much over the last 9 years.Yes, but the OGL kerfuffle seems to provoked some other game companies to step and create more open games (that seem to have a fair of public interest as per the MCDM game). This could have longer term consequences for D&D - good for gamers but may effect D&D in terms of supporting the new version of 5e and may have consequences on a financial level.
To think that MCDM or Kobold Press or Darrington Press or Arcane Library or anyone are going to release anything in the future that will actually impact D&D in a meaningful way (that Hasbro/WotC has to adjust to) is rather wishful thinking. So far that kind of things has happened one time... Paizo making Pathfinder and massively impacting 4E... but I do not foresee any other RPG being released that will put that sort of dent in 5E (the 2014 or 2024 versions.)
I mean it hasn't been lost on me that even companies that did release non-D&D games over the last decade-- like Monte Cook Games and their Numenera line-- ended up adapting parts of their line TO 5E as well in order to cash in on D&D (like so many games did back in the 3E era with d20 versions of Call of Cthulu, 7th Sea etc.) That tells me that companies are still always keeping an eye on D&D and adjusting to them, rather than the other way around.