The difference in meaning is fairly subtle.
But if he eased, his first steps would lag behind those of his competitors.
We are referring to the "steps" a person possesses, and the word "those" refers back to them. You could write this as:
But if he eased, his first steps would lag behind the steps of his competitors.
That is, a thing he possesses (steps) lag behind a thing they possess (their steps)
However, with the second sentence:
But if he eased, his first steps would lag behind his competitors.
We do not refer back to "steps" anymore, "his competitors" refers to the people themselves, not something they possess.
While not technically wrong, AFAIK, this sentence is awkward. People are similar things, steps are similar things, people are not similar to steps - so comparing their position (behind) is awkward.
An interesting note however:
But if he eased, his first steps would lag behind his competitors'.
Is possessive, and therefore correct. Though it may still sound just as awkward to some readers, and sounds identical spoken.