Is this Front-rank checkmate?

This is still a back-rank checkmate, but for Black.

In chess terms it’s a Back Rank Mate, and I think it is.

No, this is for white. white king's position is g8.(not b1)

It's still considered as "back-rank checkmate" even though we know it's clearly happening at the front rank.

How about side-file checkmates then? What do you think?

All I could think of was that the King's escape route was blocked by friendly piece.

Back rank mate is not really a mating pattern, it is the description of a process leading to the mate. When you ignore the safely of your king on the back rank, your opponent may find a combination - possibly involving sacrifices - to checkmate your king while hiding behind his pawns. Checkmate on the opposite side is not called "front rank mate" simply because there are no common game situations which lead to such a mate.

Note that back rank mates are rare in problems and endgame studies, precisely because the process which leads to it is typical for games while composers are not all that interested in it. Some mating patterns may look similar to back rank mate - like smothered mate or the mate of K+R vs K - but they arrive via a different process and have somewhat different setups.