Computers can perform such computations a lot faster than we can, which allows them to defeat even Grand Master of chess.
I believe the relative pronoun "which" refers to the entire sentence in front.
Now if "which allows" was replaced with "allowing" as:
...a lot faster than we can, allowing them to defeat even Grand Master of chess.
would it still work fine and make the same sense?
Yes and yes.
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As Ivanhr says, yes and yes.
The difference is the type of subordinate clause. Allowing them to defeat even a Grand Master of Chess is not a relative clause but a gerund-participial clause functioning as an adjunct in clause structure.