How close must it sit to the wall?

As a short throw model it is designed to sit a few feet from the screen and still project a large image. Exact distance depends on the screen size you want, so check BenQ's throw ratio for your planned screen.

Is it good for gaming?

It is a 4K DLP projector with HDR, which suits console and PC gaming. Check the input lag figure for the picture mode you plan to use, since game modes usually lower it.

Does it need a separate streaming device?

No. Android TV is built in, so you can install streaming apps directly. A separate stick is only useful if an app you want is missing.

Expect the projector, a remote and a power cable. A screen, mount and HDMI sources are separate purchases.

How does it compare with the TK710?

The STi adds a short throw lens and built-in Android TV, so it fits tighter rooms and needs no streaming stick. The standard TK710 is a long throw unit that needs more distance from the screen.