The text states that Alexander "was not asking [the troops] to take any risks he would not take himself." What benefits would this have on the soldiers in battle?

This is a technique commonly used by leaders 'to inspire' their subordinates.

Explanation:

It communicates to the soilders, or those being lead, that they're not beneath the leader (ie. the leader and those being led are unified in action). If leaders would have soilders do the same things as them, then an aire of trust and respect in inspired between both parties. This usually results in the troops giving the leader all of the effort they can muster.