I love this picture, there is seriously not enough Engie and Pyro fanart out there.

I always saw Engie and Pyro having a Father and son type of relationship. Going by his mannerism Pyro is obviously younger then Engie but that should go without saying.

Like you said a Pyro is an Engies best friend next to a box of metal and since Pyro's mental capacity is somewhat questionable I doubt he could have a "romantic" relationship so at best he'd probebly see Engie as a father-figure and Pyro would probebly be Engies retarded step child. But thats just one fan's opinion ofcourse.