Yes and no. They jump around the profit-point. They made some profit in 2019 or so, but the pandemia peaked them, not just in views and income, but also costs. The thing is, Twitch's business-model is very frail. A streamer with too many viewers can cost them more money than it brings them money. Similar, are there millions of small streamers who barely make them a dollar. And then are there also too many side-costs, like South-Korea's network-fee recently, or the too many law cases where come cranky person sues them for some nonsical reason.

And we don't know for real how much Amazon is charging them. Rumors are going, Amazon is charging them a hefty amount for servers, while other says AWS is irrelevant for their Service, so nobody knows for real, officially.

But the recent move to a different handling of video-streams is supposed to change this, as it reduce the costs on Twitch's side, and lets the Streamers pay for it themself. By which I mean AV1(?), where the streamer is encoding all streams in all resolutions, and only sends it to Twitch which then acts as a relay. Claim is, Video-Encoding was the biggest cost for them, after employees, which seems kinda strange.. But maybe it will change their game in the next years, we will see.