I use a roughly $6 HDMI capture dongle <- a $10 RCA to HDMI adapter <- an old VCR, and OBS is the capture software I use. Comes out pretty well, though you do basically end up watching each tape doing it.
Can you tell me about this 6 dollar capture dongle? How come people pay hundreds for stuff like ElGato HD whatever to capture and stream their video games? Can a cheap dongle do this too?
Apparently I paid like $15 or something, but anyways, this is what I bought, prices have changed a bit since then, but identical devices are out there under various ASINs/labels:
As far as game capture, it probably depends on a few things. Name brand definitely has significant markup, but they also include software and such as well. Note that my capture dongle here records in 1080P only, and you'll spend a lot more for 4K-capable hardware, and fancier capture devices offer HDMI pass-through so you can both capture and display on a screen, and this does not.
Now, if you want to play your games in OBS at 1080p, this might work for you, I'm not sure where performance starts to degrade for a cheapy dongle like this, but I think there's probably a good reason gaming setups use a little bit higher end setups.