While it makes sense for Apple to continue to focus the AppleTV primarily on the streaming content market, I think they could significantly expand their potential sales through gaming. Families who buy an AppleTV primarily as an inexpensive console for casual gaming would become potential customers for impulse streaming content purchases. (It's why even the most basic STBs have PPV functions.)
I agree it would be stupid for Apple to try to make the AppleTV a competitor to the PS4 / XB1. But I do think they have severely limited sales due to the restrictions they are putting on developers. The iStore description for games could clearly indicate what controllers are required / supported. The iStore app could even check what controllers have been paired with the AppleTV and give an extra "are you sure" prompt.
IMHO Apple should have created an iDevice controller app & SDK for developers to use. Multiplayer AppleTV gaming might even drive a few iPod Touch sales.
I think Apple is playing it pretty smart, actually.
They aren't betting the farm on AppleTV being a gaming platform, but they're preparing the ground for it nonetheless.
The remote restriction is so that people thinking about playing games on it won't be presented with nothing but titles that they can't even play.
The size restriction is to enable impulse buys without tying up the device for eons while a huge game downloads that they aren't even planning to play right away.
Once gaming has become established on AppleTV and there are plenty of games you can play out-of-the-box, they'll probably relax the restrictions on using the remote. The size restriction may stick around, but will probably be tweaked to accommodate developers just like the size of apps on iOS were initially restricted but later were allowed to get bigger.
Remember, it's always easier to relax restrictions than to add them on later. Once Apple gets a feel for how people and developers work with AppleTV they'll make some adjustments. They're just being initially cautious as usual to protect the user experience so people don't get turned off by it right out of the gate.