Key word is probably 10 landings a day, not 10 flights. Not sure why anyone cares about takeoff...though the wings could be full of fuel and their heaviest at that point. But it's during landing that they're supposed to get the biggest dynamic loading. Often the plan is to have fuel tanks not so full when landing occurs. In turbulent air, you'd think it could get quite bad. My memory is a bit blurry but I seem to remember these things designed to survive a 30 ft free fall onto their landing gear. The static equivalent g load, and on the pickle fork, is probably way up past 10 g's, with probably a good FS of 5+.
How many touch-and-go's are done in a day if somebody's practicing?
737-600, -700, -800 & -900 are all 737NG's. I'm not aware of UA having any -600's. In any case, there might be 7000 of these out there. They've been in service since late 1998. How many have had over 35000 cycles? Potentially quite a few.
35k. 90k cycles. I'm a bit surprised the fatigue life is that low. That's low cycle fatigue in my book. Are these polymer composite laminate structures? I don't know.

shhh... Almost every 737 in the sky is a 737NG right now.

I wonder what the acceptable crack size, where and in what orientation, is before the books associate them with an unacceptable crack opening energy.