"Seat at gate" means you will be assigned a seat at the gate. Nothing worth overthinking in the term.

Why? Could be any number of reasons, but none matter as you will be assigned a seat at the gate.

You should make a point of asking and not relying on the GA to get this done in a timely manner.

Could wind up in the worst seat on the plane or there could be a lot of others upgraded and a bunch of misconnects and you will wind up in a C+ aisle.