The to in "as if to" isn't a preposition, it's the start of the infinitive noun ("to flee").
As Daniel Lloyd very tersely pointed out, if you were to insert a were in the sentence, you'd have to change the rest of the verb to match.
Overall, "as if to flee a tiger" is an infinitive phrase, modifying the verb in the main clause. In contrast, "as if he were fleeing a tiger" would be a subordinate clause in the subjunctive tense.
Of course, both express the same semantics (meaning), however the infinitive sounds a little more terse and immediate compared to the subjunctive.
If you were to remove the hypothetical, you would have
He runs to flee a tiger.
Again, "to flee a tiger" would be an infinitive phrase describing why he runs. Compare with:
He runs; he is fleeing from a tiger.
He runs because he is fleeing from a tiger.
Two separate clauses, optionally linked by a conjunction.