"Heart" and "Soul" are funny descriptions for things. A lot of people will say they're meaningless in this context, but as an artist I can understand the sentiment behind those phrases.
My own take on it is that a game with "heart" or "soul" is a game "made for all the right reasons". Basically, they weren't produced because of clinical or mathematical reasons. There was a clear drive, a creative force, and a desire to reach other people on meaningful levels through their works. It's quite easy to tell which games have it and which games don't.