Yup, you're missing something. It's Quota as in a quota game, not Quote. A quota game is a gambling game in golf. Whoever shoots the most over their 'quota' wins. Handicaps can be used to establish quotas (handicap subtracted from 36) or you could play a few rounds to establish a quota.
In my post the 14 meant you cannot go below a 14 quota. Players compete over 18 holes and whoever is the most over their quota wins. You can pay out different places depending on how many players etc..
Let's say you're 15 handicap. You'd be a 21 quota, meaning you need to get 21 points to make your quota. 4 points for a birdie, 2 for a par, 1 point for a bogey and zero points for doubles.
Let's say you get 25 points. You'd be plus 4 and depending how your competitors did you may win money. It's a fun game where different handicaps can compete against each other fairly.
In my post I was explaining how short hitters moved up and were able to score better (instead of hovering near the minimum 14 quota). Their quotas got higher because of that. I should say whatever tee you play your quota would be reflected by that tee. In this case they had more fun because they could score better.
BTW, it's a senior group (over 55) and these guys are in their upper 70's and 80's.
Hope this helps.