It works very well for game streaming, but it turns down the quality for me. I haven't tested in a while, but (game depending) it works VERY well. I played Batman Arkham Asylum all the way through using my Shield for Game Streaming. No issues there.
I tried playing Battlefield 5 and it turned down the quality too much. Plus, I'm not a fan of FPS using a controller anyway.
As for being "overkill" for a streaming device, yes, but if you have high quality local video and want audio to play back bit-streamed without being decoded or downgraded to losless, then it's one of your only choices.