It can mean either although in this sentence it's likely to mean the former.
I hear it as mé - it's shortened a bit because it comes right up against mo, but that's not dialect dependent.
The Rugby reference is explained in the links above - the Irish Wolfhounds is the nickname for the Ireland A team, which was traditionally made up of players who were on the fringe of qualifying for the Senior team.
Neither the dictionaries nor tearma.ie offers a term for a wolfdog hybrid (the EID gives “wolf-dog” as a synonym of “wolf-hound”, cú faoil ), so madra faoil might also not be interpreted in a hybrid sense. I don’t know if madra mic tíre would be distinctive enough. Faolchú is already defined as “wild dog, wolf”, so I don’t know if it could be stretched into “wolfdog” also.