It's not a minimum before a check is issued. If you do not have a certain number of annual listeners on a track you never get paid out for it. If you had 100 tracks that were each streamed by 999 listeners who each streamed them 100 times per year every year, Spotify will no longer pay you a dime, ever.

I think a key point of confusion is in the way they presented it. They talk about how many songs have "less than 1000 listens" and that those would only make $3, but then their new policy is to deny payment for "less than 1000 listeners." If each of those listeners streamed the song once per month, you're talking closer to $40 than $3, and that's on a per song basis.