People used various video streaming services other than Youtube back in that day. Google's own video streaming thingy was a shitty competitor; Viddler, Blip.tv, and Vimeo were others. Screenshot let's plays [56k catchphrase] were also common, and probably still are.
What made Something Awful's let's plays notable was quality control, at a time when quality control did not otherwise exist anywhere in the Let's Play world. You had people using terrible capture software or even camcorders to run their video Let's Plays, doing episodes where they literally just died fifty times in I Wanna Be The Guy and made no progress because the game crashed, doing episodes where the mouse pointer was clearly visible, providing terrible commentary about how their cat gets high off the smell of their sweat or whatever the fuck, responding with extreme hostility to any criticism, getting interrupted by moms and/or lumberjacks, and generally being unwatchable. SA had a brutal culture of critique, which was often counterproductive (the LP Sandcastle basically functioned like this site's Proving Grounds used to and was thus very good at making people reluctant to ever post any new threads at all) but generally meant that the Let's Plays that you clicked into weren't going to completely suck. That was that subforum's draw, as was Retsupurae, which existed to ruthlessly mock bad Let's Players on and off the site.
Lowtax made an effort to get into Let's Plays in 2013, by playing a fairly low-quality indie horror game called Cry of Fear and bringing Shmorky in to commentate alongside him. LP was becoming increasingly pozzed at that point, and the thread was full of people saying that shmorky sounds so cute he's like an adorable little teddy bear that you wanna snuggle uwu. This adulation very openly contributed to Shmorky's steady mental decline, which was observable as the LP progressed and as Lowtax and Shmorky began playing other garbage games together while Shmorky shrieked in an ever higher pitch.