It's not possible right now, but it's an idea. There's a "mobile friendly" checkbox for HTML5 games after all, we could use that. I guess the idea was not to filter by default because you might still want to access the game page on mobile even if you can't play the game, e.g. to download a file or leave a comment.
The not being able to filter for issue sounds like something that could be fixed rather easily (once the admins aren’t drowning in work anymore). I’ve written up a suggestion about that - based on what I understood. If any of you have something to add to that, please feel free to do so.
