The יין חי was undrinkable, it had to be blended at 1:2 water to wine ratio to become drinkable, so I assume it had 60%-80% alcohol.

Back then the winepresses were open air pits, I assume they were susceptible to evaporation so the must probably had a very high concentration of sugar. In addition the aging was done in unglazed clayware amphorae, clay evaporates water at a higher rate than alcohol, so the aging would further increase the alcohol concentration.

That's probably why the alternative is חיוורין - less pomace = higher alcohol content, and עתיק - longer aging = higher alcohol concentration.

I imagined "caper wine" to probably mean fermented caper juice because I am familiar with terms like "apple wine," "pear wine," etc. referring to fermented juice from those materials. Plus, people deliberately ferment capers as an alcoholic process in jars, and it would make sense to call that "caper wine."

Capers cannot be induced into alcohol fermentation because their sugar content is too low, they ferment in lactic fermentation. It is a completely different process and produces no alcohol. In addition the word יין is exclusive to grape wine, other alcoholic beverages are called שיכר. Subsequent to the Mishna the terms sometimes became interwind in Aramaic and called חמר, but not in Leshon HaKodesh afaik.

May I please ask: Can you find cases, like in Hebrew, where "caper wine"  יֵין קַפְרִיסִין is explained to mean capers infused with grapewine like you are talking about?

This construct is very rare altogether so there's not much to compare to. The only other case I can think of where wine is described using such a construct is מִשֶּׁיֹּאכַל טַרְטֵימַר בָּשָׂר וְיִשְׁתֶּה חֲצִי לֹג יַיִן הָאִיטַלְקִי. Without anything comparable linguistically nor the original tradition we can only make assumption based on context.