Is this a checkmate?

Checkmate.
If the Black King were really free to step into the Bishop's check (by taking White's Queen), then why couldn't the White Bishop do the same and take the King, ignoring the Rook's attack?
Sauce for the goose is sauce for the gander...

If you play it out, assuming that the king could be taken, black king takes white queen, then black bishop takes white king, and only then could black rook take white king.
The sequence of events without the the “can’t move into a checked position” rule, leads to the black king being taken first.
The bishop is pinned by the rook. So will it be considered a checkmate or the black king can still take the white queen because of the pinned bishop?