The pKA of an alkyne should be around 25.
A diarylmethane (that you might assume to be a decent approximation of PhCH2-vinyl-vinyl - or could you?) around 34.
So apparently there is no question, the alkyne is more acidic.
But I have to admit I had to look it up, that's the kind of thing you forget if you only study it at school and then don't apply in practice.
You can't really derive it from pure reasoning, because OK, they tell you the alkyne has a strong 's character', therefore its carbons are very electronegative, therefore the proton is very acidic, but at the same time you have an extensive conjugated system that should provide very good stabilization for the anion formed on that CH2.
That's all qualitative information, but how do you quantify it? It's one of those things you need to learn by heart, full stop.
Therefore, a rather malicious question in an exam, I'd say.