Projection is a defense mechanism that involves taking our own unacceptable qualities or feelings and ascribing them to other people. For example, if you have a strong dislike for someone, you might instead believe that he or she does not like you. Projection works by allowing the expression of the desire or impulse, but in a way that the ego cannot recognize, therefore reducing anxiety.
They're doing it wrong, since it does not seem to be reducing the left's anxiety.
Someone who is pathological may do well at it, but there's no sense in calling a skilled politician pathological simply because he or she is on the other side.
But people do make charges like that. It's not because of something inside of them -- or it doesn't have to be. It's also all part of the political game.
Chances are, if one plays the game long enough, one probably has things to hide and a share of hypocritical behavior, but it's more the way the game works, rather than a sign of deep pathology or inner psychological drama.