I think it will affect the supply rather than the demand of HTML5 games initially. Firefox OS has a very small market share in comparison to iOS and Android so while there are more folks playing HTML5 games, it isn't a huge amount. However, big name companies backing HTML5 like Mozilla with Firefox OS and Samsung/Intel with Tizen, they're doing their best to get popular games ported over to HTML5, as well as more new content.
For example, the Tizen App Challenge (https://developer.tizen.org/contests/tizen-app-challenge) is offering some pretty large prizes for HTML5 apps/games.