Because Amazon and Apple are dipping their toes into that pool and Google is playing catch-up on the set-top-box market instead of leading.
They sell games. They sell hardware on which people play games. They sell a set-top device that plays games. But they don't sell an actual controller for that device.
But they dip into all markets. Someone said they are a "me too!" company that hurriedly adds products in a particular market area, then abandon maintenance of it after a while.
Their core competency is marketing / search / ads, so I suppose the entire Android system and any hardware could be considered a side show?
BTW, I am a happy Android user (other than Maps and Talk, which have gone down the toilet).
They sell games. They sell hardware on which people play games. They sell a set-top device that plays games. But they don't sell an actual controller for that device.