My earlier impression that Nima's slogan "spacetime is doomed" could potentially lead to a reformulation of string theory, is wrong and an overinterpretation of Nima's very enthusiastic comments. As Lumo says in his nice clarifying comments, it is rather the other way round and "spacetime is doomed" is in fact a result that came out of string theory quit some time ago already:
The fact that spacetime is doomed is one of the main results of string theory, primarily; twistor variables and other things are just individual manifestations of this stringy conclusion and it would be silly for Nima or anyone else to claim the priority in the "spacetime is doomed" paradigm shift which was derived and said a decade before him by string theorists such as Seiberg and Witten. So your causality is upside down. Your question is like asking what would happen to Einstein's research if the world respected relativity. Well, its key epoch would victoriously end.
Concerning the particular wording "spacetime is doomed", you may see that it was used by David Gross in 2004, right after he won the Nobel Prize:"Everyone in string theory is convinced that spacetime is doomed." The statement "Space and time may be doomed" (Witten) and "I am almost certain that space and time are illusions" (Seiberg) come from the 1990s, see many google results.