Sentence

We are doing no favors to the young men if we let them believe that a game shall set them free.
I am saying the clause "that a game shall set them free." Is a dependent clause am I right?

There are two dependent clauses in that sentence, one inside the other.

We are doing no favors to the young men = independent clause

if we let them believe (that a game shall set them free) = 2 dependent clauses.

"if" and "that" are the words that signal to you that a dependent clause is beginning.