What exactly means "in play" ?

Are cards attached to discard pile and domains in play ?

Regards

In Play is the Play Area, so no, nothing associated with Discard piles is "in play."

So dose it means that cards attached to discard pile( for example Snow Grave) are untouchable by Dimensional Rift ?

Snow Graves is in play as long as it is attached to the discard pile and not in the the discard pile.