I see the focus here is on
team winning streaks. If so, then how about Wayland Baptist Women's college basketball: 131 consecutive games, starting in 1954.
Individual winning streaks? Jahangir Khan:555 consecutive wins in professional squash.
Jahangir Khan - Wikipedia
In any event, while these absolute numbers are certainly impressive and entertaining, they cannot tell us too much without knowing, among other things, the strength of the competition and parity among competitors. In this respect, all other things being equal, the Cleveland Indians' 21-game streak in 2017 is more impressive than, say, the Cubs or Giants streaks of decades past. The difference between the best and worst is demonstrably less today than 80+ years ago, while the overall quality of play has undoubtedly increased.
p.s. I disagree with the decision to place UCLA's 88-game streak at No. 1. No rhyme or reason why that would necessarily be more impressive than some of the other (longer) streaks, including UConn's 111 game streak.