It's also a world where the Soviet Union and PanAm both still exist!
I'm thinking, while the survival of a particular airline is probably not important, the USSR is. Especially if we include the context of
2010 as part of the backstory of
2001--the Russians are a side element in the earlier story and could in principle be replaced with any non-US colleagues of Dr Floyd asking him tricky questions, but central to the later one.
How plausible is it that, without actually beating Apollo 11 to the Moon, the Soviets stay doggedly in the "space race," sending their own successful missions to the Moon, and that this determination of theirs to stay in leads US political leadership to commit to an ongoing expansive US effort rather than retrenching once the "Moonshot" is accomplished? And in turn, that there are enough positive benefits to extensive and expanding manned presence in space that both the Western nations and the Soviet sphere feel the investment was justified and should be sustained on an ongoing basis, and indeed, what are the odds that sufficient benefits, if only political, redound to the Soviet regime that it manages just sufficient reform to stay viable and stable, so that by 2001 a patriotic American scientific bureaucrat like Floyd has pals among his Soviet counterparts, friends whose careers in turn are helped rather than hindered by their close contact with an American?
To some extent this latter sort of relationship was hardly unknown OTL, but sometimes bad things did happen to the Russians involved; I take Floyd's relationship with the Russians he meets on Station V as evidence that ITTL the USSR in 2001 is a pretty self-confident regime, one that doesn't feel threatened by personal contacts between its citizens and Westerners. This implies a rather stronger economy than OTL. (If I assume that, then the conflict between US and Soviets which plays such a strong role in the movie version of 2010 (not in the book though, which I'd prefer as the real canon) seems most likely to reflect an unreasonable American regime, perhaps one that is doing badly in domestic terms. Or of course just ignore the movie and stick with the book!)
The tricky bit here is, trying to figure out why humans in space works out so profitably for both East and West.
If it does I suppose most of the rest follows pretty naturally; aside from HAL itself, the high-efficiency plasma rockets or whatever they are that propel
Discovery, and of course the Monolith Aliens themselves, there isn't much in the original movie/book that doesn't have a clear basis in perfectly attainable technology. We could have had a Space Station V, the presumptive 4 stations before it, and a Moonbase much like the one shown by 2001 with enough investment, and I suspect not even an investment that would greatly warp the economy. (Not so sure about that rocket-lifted Moon transport craft though--Clarke in the book had it be a bus on wheels, and I'd think if one were in a hurry to get somewhere and using rockets to do it, you'd have a suborbital craft that looks like an Apollo LM rather than something that appears to be firing rockets continuously just to hover! Looked cool though).
But it is hard to imagine why any society is going to invest so much unless there is a clear and immediate payoff; using paranoia about the other side getting ahead only works so far.