I gather that the key insight of updateless decision theory is to maximize utility without conditioning on information about what world you're in, and the key insight of timeless decision theory is what you're describing (Eliezer summarizes it as "Choose as though controlling the logical output of the abstract computation you implement, including the output of all other instantiations and simulations of that computation.")

I think Eliezer's summary is also a fair description of UDT. The difference between UDT and TDT appears to be subtle, and I don't completely understand it. From what I can tell, UDT just does choose in the way Eliezer describes, completely ignoring any updating process. TDT chooses this way as a result of how it reasons about counterfactuals. Somehow, TDT's counterfactual reasoning causes it to choose slightly differently from UDT, but I'm not sure why at this point.