Unfortunately, as reported, there might be something missing, since the first player may just remove $99$ heaps at his first move, leaving the second player with no move.

I think the intended interpretation might be that heaps still exist even if they become empty. So if the first player removes 99 heaps (or otherwise leaves at least one heap empty), the second player can take all the remaining stones and win, since he would not have touched one empty heap. If this is the case, the problem is still rather easy, though: the second player wins iff all 100 heaps have the same number of stones.

The Russian version says:In one move, it is allowed to take from the table an arbitrary (non-zero) number of stones from any number of piles not exceeding 99