Ok, so, Remotr...
Turns out the streaming server application works on windows 7, 8, and 10, but the client is only available for Android, IOS, and the windows 10 store. So, still not quite what I was looking for. But I gave it a try using my phone anyway.
It is ad supported. Meaning you'll see an ad every time you launch a game or close out of one. The preroll ads are all under 15 seconds, and the postroll ads are closeable after 15 seconds.
Setup is effortless. You install the streaming server application on the gaming computer (which is just clicking "next" 3 times), then login/create an account (which only requires an e-mail address and password, and takes no time). Install the app on your client device, which is just as easy. Login there. It immediately sees your host pc, no problem. In fact, it enumerated all my games instantly, be they on steam, battlenet, or whatever else. So you pick your PC to stream from (yes, you can have multiple ones and choose from them), then pick your game, watch an ad, then you're off. The only caveat is, it sometimes doesn't work if your desktop PC is locked - and the times it does work, the first thing you'll have to do on screen is unlock the PC, and then Remotr won't re-lock it for you when you're done. However, Remotr does also come with a built in "desktop" app that works more or less as well as windows remote desktop, so you can get in to unlock and relock that way - although, it's not as advanced as, say, TeamViewer, and doesn't support switching between multiple monitors and such.
So, how did they fix the lag issue?
Wellllllll they didn't, really.
Playing Left 4 Dead on my phone reminds me of playing Quake 2 deathmatch on my 28.8 modem back in 1996. There's about a half-second of input lag, and on top of that, a further second of sound desync (as in, sounds are played a half second after the action that causes the sound happens on screen, which itself is a half second after you input the click to fire the gun). It's not IMPOSSIBLE to play this way, but it isn't what I would call pleasant.
So, if you're not on your local network, FPS games kinda go out the window.
However, it's still pretty good for some other games. Darkest Dungeon seems to work ok. Admittedly, it's a turn-based game, but the input lag is much less noticeable, and it also looked sharper I think, probably owing the game not being a first person camera changing viewing angles constantly. Stardew valley and Undertale are playable, but the input lag is a little bit of a factor there, too, when it comes to movement - especially on Undertale's bullethell dynamic.
Another thing is, this wants a gamepad controller really bad. While most mainstream/multiplatform games will come with a preset bunch of onscreen/touchscreen controls, a lot don't. L4D and Darkest Dungeons I had to build my control UI from scratch - which wasn't difficult, really, other than having to remember the all keys I needed to play without being at an actual keyboard, but it was time consuming. It does, thankfully, remember your UI setup automatically so it is still there when you come back next time.
So, yeah. That's basically it. You pretty much need to be on the same LAN as the host PC (though it will let you try from anywhere, and I respect it for at least letting me try, unlike, say, Steam In-home Streaming, unless you want to screw around with Hamachi), and it works best with a game controller.
Though, I do wonder how much of the input lag comes from the latency inherent to being forced to use wifi on my client (since I can't exactly plug an ethernet cable into my phone), and if a PC-based client can shave 10 or 20 ms off its ping time for not being wireless, it might help some. Or maybe not. I don't have a windows 10 machine to test it on, so c'est la vie.