alt Hacker News[ made this a top-level comment as I don't see it mentioned in other comments: ]
The result doesn't actually apply to _all_ algorithms, only oblivious ones. Oblivious algorithms are ones where step i does not depend on decisions made in steps j < i. Almost all useful algorithms are non-oblivious, with some notable exceptions [1]. This work is a step forward towards proving the result for the general case, with little practical usage (and that's perfectly okay).
It applies to any algorithm that can be implemented with a multitape Turing machine, which is still quite a few of them. The obliviousness requirement is only for random-access machines.