A few years ago I had the same thought about Carmack. I wondered why he seemingly abandoned his vision for space travel by returning to work in the game industry on Rage. I figured Carmack probably realized that Elon's SpaceX was going to "win the race" and gave up. Or maybe Carmack is just getting old. Either way, he's still one of my heroes.
I wouldn't be surprised if Carmack heavily inspired Musk. If not just with shareware, and online payments, then with rockets.
Also, the public .plan files he published in the 90s heavily inspired the web log/blog craze :)
Elon on the other hand, has been willing to double down on bets involving 100's of millions of dollars or more. That speaks to a very different view of risk/reward between them (and not one I think is negative to either side).
Also, while Carmack is certainly enormously respected in his field, he hasn't worked much outside that. Elon's track record has diverse successes, and I think that means it's a lot easier for Elon to convince investors to join his endeavors.