Personally I would give it for going above and beyond as it was stated “going out of ones way”. I thank my team daily for the hard work they do doing their jobs. If it’s someone from another dept, I email their supervisor and include the GM. This is just another way to recognize that. 

“Can employees hand out Peer Praise to their supervisors? I note the use of the words "co-worker" and "peer."

Supervisors have the books so I’m not sure. 

“It sounds like department heads can give each other Peer Notes.” 

I suppose if they wanted too.