Other sorts of lock could be used to lock a gate; however, the typical 19-early 20C garden gate lock is a mortice-style bridge ward lock, but they were almost as often fitted as rimlocks too. They are usually two bolt or deadlocks. They also usually have a longer bolt(s), which when withdrawn still protrudes from the lockcase. As mortice fitting, they have a rather short key shank, or longer if rim fixed. The wear on this suggests either abuse, or the bolt was binding? The style of key suggests later rather than earlier. These were exported to the US, so quite possible it was, as reported, a gate lock key.
For the record, there was another form of ‘gate lock’, used on farm gates. Like an old external surface-mounted chest lock, such as used to be used on luggage before modern plastic suitcases - but with the hasp on a chain with its end fixed to the gate. A good deal more expensive than using a chain and padlock, probably why it fell out of use.