One can have no "trouble with rhythm" and yet meet the DSM-5 diagnostic criteria for ASD; one can have immense "trouble with rhythm" and yet not meet those criteria – that's because "trouble with rhythm" is not part of the diagnostic criteria, indeed if you read the DSM-5 section on ASD it never even discusses that topic, "trouble with rhythm" simply isn't part of the DSM-5 definition of ASD. At best, it might be seen as an "associated non-diagnostic symptom", something which may occur in some people with ASD (possibly even at a higher rate than in people without ASD); but it is simply a mistake to reason "person X doesn't have symptom Y hence X cannot have ASD" when Y is not a diagnostic symptom.
I don't know whether Stallman has ASD or not, but his conclusion that he doesn't seems to be based on incorrect information. Given that, I don't think we should put much weight on it.