What is the meaning of this pseudo-code function?
"Implies" in the English language indicates that there is room for subjectivity. But this is not standard English you're looking at. When you read A⟹B as "A implies B" in Discrete Mathematics, it is just another way to say, "If A is true, then B is true." Formally, this is called material implication.

So the two ways you thought to read it are the same - as far as Comp.Sci. goes. Left to right and minimal imagination it reads (out loud), 
"Return the truth of this assertion: For all q-sub-i that are members of subtreeNodes of q, isLeaf of q-sub-i implies eof of T-sub-sub-i."