A hobby is something a person does for personal pleasure as opposed to financial gain. The term "unique hobby" has a couple meanings. In general, it is a pastime that is not shared by a lot of people. This phrase also describes a hobby that doesn't fit a person's reputation.
Collecting promotional table tents is a unique hobby because it is not something typical people would do for fun. Collecting Pokemon cards is not a unique hobby based on common convention. However, it is a unique hobby for a professional athlete or actor, especially when the hobby does not fit his personality or persona.