Learn Arabic (Modern Standard): إذا انسحب الخصم، انتهى دوره.

This is a key rule for Arabic 'if' sentences! When using إذا (if) for a real or likely condition, Arabic traditionally uses the past tense for both the condition verb (انسحب) and the result verb (انتهى). Even though the verbs are grammatically in the past tense, the meaning is understood as present or future.

Why does the verb come before the subject in both halves of this sentence?

Arabic naturally prefers to put the verb first (Verb-Subject-Object order), especially in verbal sentences and right after particles like إذا. So the sentence is built literally as 'If quit the opponent, ended his turn.'

What does the suffix at the end of دوره mean?

The word دوره is made of the noun دور (turn or role) plus the attached pronoun ـه (his). Since the opponent (الخصم) is grammatically masculine, we use the masculine 'his' suffix to say 'his turn.'

I know the root word سحب means 'to pull.' How does that relate to انسحب (quits/withdraws)?

انسحب is a Form VII verb, which adds a specific prefix to the root. This form often makes the action happen to the subject itself (reflexive). So if the base verb is 'he pulled,' this form essentially means 'he pulled himself' — which perfectly translates to withdrawing, retreating, or quitting!