If your connecting flight departed at 1510, I think the gate closes time should have been 1455. Are you sure you read it right?

But I don't understand the question, in any event. You knew that your flight was departing at 1510. Why would you have done anything other than what you did? Making arrangements for an alternative, later flight is something you do only after you know for sure that the aircraft has gone without you, not simply because your boarding pass says that the gate closes at a particular time.

And what were you doing between 1425 and 1502 that took so much time, considering you were making an airside connection in the same terminal? It's just a question of going upstairs in Terminal 4.