First of all, I promise you're not a genetically inferior (aside from the cancer thing, which I'm not trying to downplay - that's got to be a killer physically, mentally, emotionally, spiritually, and every other -ally). I wasn't even a varsity athlete in high school, thanks to asthma* and spending more time in the library than the weight room.
1) In my case, I was alternating between bases and plate, so I wasn't geared up for all 7 (though a guy on the field next to me who is fit and in his mid-20's did 6 in a row on the dish). So that certainly helps. I did 3 back-to-back plates once (showcase ball, so they were moving along), and I did it, but I don't have any desire to attempt 4
2) These are also time-limited, so you don't have any 4-hour marathons.
3) For me, it's much the mental challenge. Can I still stay as focused and "on top of my game" in game 7 as I was in game 1 or 2? I think those kinds of things will help me out when I'm in a bad situation. "C'mon, you've survived worse than this, suck it up."
4) Physically, yeah, I'm a little sore and tired today, but you'll be surprised what you can do when you don't have a lot of other options. Work still needs to be done, so I do it. And dang, the hot shower felt great last night, nearly as good as the pillow did a few minutes later. There have been days when I've pulled the car into the driveway, turned off the ignition and just sat there a couple of minutes working up the gumption to actually get up.
*which I've pretty much "grown out of" I have to take an inhaler usually 2-4 times per year now, and no other regular medications, but I'll still never be a long-distance runner.