I think you might be having problems because you're assuming the は is marking the subject when it's actually marking the direct object. That is, it's replacing a を. (See also this question.)
Working out from the middle:
一人一人がどちらを選ぶのか
This is an embedded question acting like a noun phase. (See this question ) meaning "which one each person chooses." Normally as the indirect object it would take a に afterward, but nominalizing questions in this way usually deletes the を/が/に.
国の勝ち負けだけじゃかく
"not only the victory/defeat of countries", i.e. the outcome of the war between the old country and the rebel country
この戦い
the fight (for independence)
委ねている
委ねる{ゆだねる} generally means to completely entrust something. That action requires three things: the actor/subject, the trustee/indirect object, and the object entrusted. There are only two of those in this sentence though: the object (the fight for independence) and the trustee (that giant composite thing between は and 委ねる). You'd have to infer the subject from context, but given the speaker I'm betting it's something like "we" or "the rebellion".
All together and smoothed out a bit:
"We're entrusting this fight (for independence) not only to the (battlefield) victory of our country, but also to which country each individual person chooses."
I think the speaker is trying to convince the protagonist that their decision of which country to support is significant—they can't say that what side they support doesn't matter and they're only in it for personal reasons, because the rebellion's success relies on individuals' decisions just like his. Deliberately, even, because its success is being partly entrusted to such decisions.
Edit: added ref for は replacing を