Spotify is not profitable right now; their current revenue doesn't come anywhere close to covering their costs. The only reason they're able to survive is investors holding on to the belief that, some day, it'll be possible to actually make the numbers work.
Musixmatch has a free, public database where lyrics are displayed. To contribute to the database, users can sign up and contribute lyrics, synchronizations, translations, and structuring to get points and move up levels. Musixmatch's points have no redeemable value, but are instead a marker of a particular user's contributions.
It is fucked up that the fans who are transcribing do not get a cut, but it's not like they were misled to believe they would make a cut before they started doing it. The people doing that are doing it out of a passion for the music.
I'm not saying they shouldn't be paid of course they should, if it was up to me I'd say make them all rich. I just think it's a stretch to imply that Spotify is stealing anything here
The writers almost certainly do get a cut. Musixmatch does not own the copyright to any of the lyrics, and as such, negotiated with the copyright holders in order to be allowed to store, display, and sell access to the lyrics. This almost certainly involved some amount of money changing hands.
Spotify is paying money for access to the lyrics and using that as a feature in their product. A chunk of that money is almost certainly going back to the actual writers.