[jeroenhd]

Steam Link and the many other remote gaming software solutions can easily take care of the streaming part. All you really need is a tablet with a decent controller attached to it.

The Logitech G Cloud may fit your use case. Though, for that price, I don't know you wouldn't just buy an entry level Deck. The Deck's 800p screen isn't the highest quality but I'm not sure if I'd rather spend as much money on an alternative that's useless on the go.

There are also special grips out there for tablets and phones to add controller functionality; that'd probably be a lot cheaper and easier if you already have a big phone or a tablet.