A: To review, the Time Loop Power Action in Chrono-Trek says:

Play at ANY TIME to repeat the most recent game action taken by another player. If they played a card, perform that function again as if you had played that card. If they played an Artifact, replay that Artifact as your own.

It may depend exactly what action you’re copying, but certainly in the case of an Artifact play, the Time Loop is functioning EXACTLY like the Surprise called That’s Mine! and, as such, we would rule that its “any time” play and the resulting outcome would result in a successful prevention of someone’s winning play. Just like a Surprise, however, it must be played IMMEDIATELY after someone plays their Artifact for the win. If you wait too long, only playing it AFTER you realized that was their winning play, it’s too late.

There are probably other cards you could copy the action of in this Surprise-like interrupt way which could also prevent a win, but we’ll address those in other questions as they arise.