Except you have to offer more than "better game performance on occasion." The BEST you could hope for, in that case, is a dual-boot form tech-savvy folks. How is SteamOS, meant primarily for gaming (not sure of its capabilities outside of gaming), going to even challenge Ubuntu or OSX (let alone Windows), when the best you can offer is occasional game performance?
Yeah, gamers are usually the tech-savvy folks who influence the masses (family and friends). But what gamer's going to recommend an OS only good for slightly-optimized gaming, when the people who ask for an OS suggestion don't want something primarily for gaming (if not solely for it)?
Google competes with Apple because Apple's model demanded competition. iOS devices come in one legitimate type of hardware. It sells at one price point. It only looks one way. Android offers something that can be played with by the tech-savvy, and it's grown to the point where the masses won't miss out on apps, if leaving iOS. Android came out at the relative start of smartphones, like iOS, and took advantage of a new market. PCs are a dying market, if anything.
On top of that Android, has backers galore. Samsung thrives off of it. HTC is arguably a lost company without it. The same could be said about a lot of mobile hardware divisions (Motorola, LG, Sony). PC makers aren't really clamoring to support Linux. Gamers also have the option of building PCs to their liking, while mobile devices basically come in a mostly-identical set of specifications, based on price points.
Android thrives because it can hit price points iOS ignores. PCs are customizable at several price points (basically EVERY price point), so they don't leave a gaping hole in the market like iOS does.