Thrill of the Hunt

I play Alpha Strike targeting my Master Yi, Unstoppable and splitting 12 damage among three of the four enemy units at battlefields. If my opponent plays Flash in reaction to my Alpha Strike, moving two of the targeted units to base, can they then play Repulse and counter my Alpha Strike?

No, they cannot play Repulse targeting your Alpha Strike. (Except if both of the other chosen units have changed to a non-board zone, such as via the effect of something like Grim Apothecary's play effect, Heedless Resurrection's additional cost, or the instructions of Thrill of the Hunt.)

A spell that targets a game object creates a targeting relationship between it and the targeted game object. As long as that targeted game object remains on the board, that relationship is maintained even if the target no longer fulfills the targeting restrictions of the spell. Even if the units in this example aren't at a battlefield anymore, they are still being chosen by Alpha Strike. We know this is true because the spell remembers that it is targeting those units if they happen to fulfill its targeting restrictions again per rule 359.3.e.3. The only exception to this principle is if the units change to a non-board zone-in such a case, they are no longer the same game object and any relationship between them and the spell that targets them is severed. Even if they returned to the same battlefield, they won't be legal targets and the spell won't be choosing them.

359.3.e.3.If a target ceases to meet the targeting requirements while the spell is on the chain, then meets them again, it's a legal target.

It can help to visualize Alpha Strike's targets with a colored arrow pointing from Alpha Strike to those units. Even if the units move to base and are no longer legal targets, they are still being chosen by Alpha Strike; we can imagine that the arrow is greyed out, but still present. Meanwhile, if they moved to a non-board zone the arrow would disappear entirely, since the game object it is connected to no longer exists. Repulse cares about the number of those arrows that point to friendly units, not the color of the arrows.

359.3.e.16. If a Delayed Ability's duration has ended before it was generated, the Delayed Ability is not generated and any instructions related to it are ignored. Example: Targon's Peak is a battlefield that reads in part "When you conquer here, ready up to 2 runes at the end of this turn." If Targon's Peak is conquered during the Ending Phase after the beginning of the ending step, such as via an effect like thrill of the Hunt, the delayed trigger will not be generated. Example: Akshan, Mischievous reads in part "When you play me, if you paid the additional cost, move an enemy gear to your base. You control it until I leave the board. If it's an Equipment, attach it to me." If Akshan leaves the board in reaction to his play effect, the delayed passive ability "You control it until I leave the board," will not be generated. You will not gain control of the targeted gear even for a moment.