Trump may have started it and may be crowing that Biden couldn't stop it, but that's just not true. Biden could have run the withdrawal very differently if he wanted, or chosen an alternative path.trump started the withdrawal, he said so himself:
But either way, this outcome was going to happen sooner or later.
The Doha deal was rubbish and gave the Taliban legitimacy it shouldn't have had, and in true US foreign policy tradition ignored the actual government of the people it concerned. However, even considering the deal I think it could well be argued that the Taliban haven't really stuck to it and therefore US shouldn't necessarily have been bound by the terms.
Even if the government was always going to fall to the Taliban (which I'm not sure is actually the case had a different path been taken), the withdrawal could have been managed in a much more organised way which would have allowed all those eligible the chance to leave the country.