Irrelevant output values will make it harder to train, yes.
The output does not necessarily have to be 1s and 0s. In fact, if you're just treating each output as a binary bit then it's probably a bad idea because each bit of the output is a fairly arbitrary value compared to the semantics you're trying to train. For example, the difference between move 127 and 128 may be minor but the output is almost entirely different. You'll be asking a lot of your hidden layers to make sense of these arbitrary divisions. (Gray code may be a better answer in such cases, but don't quote me on that.)
To adequately address this - or in fact, most AI questions - it is important to know more about the representation of the data. Of the 130 outputs, is there any correlation between them? If so, is there a way to represent them that makes more sense and which makes similar numbers have similar semantics? (eg. You wouldn't represent a position on a chessboard as a number from 1-64, you'd use 2 numbers from 1-8.) If you can find an output method that more closely relates to your data's semantics and has less in the way of possibly redundant outputs, then training will be more successful.