What you're witnessing is a barrel vault configuration. It is a perfectly legitimate style of oven, even though as you rightfully realize it differs significantly from a pompeii style pizza oven.
The barrel vault configuration does not have the vortex of fire up top that leads to a white-hot oven. The central chimney draws off a lot of that heat. It has "cold" spots. All of these are considered benefits if cooking pizza is not your only aim. Bread bakers, pie makers, barbecuers, etc will appreciate the temperature differential and the radiant heat as opposed to the direct flame vortex of a round oven. Pizza bakers want it hot, white hot, everywhere, with no loss of heat. It can be 24 hours before a pompeii oven is cool
enough to make bread or pies.
Personally I like the round chamber with the antechamber which houses the chimney, but I'm all about pizza first and bread second.
I can't speak to the masonry. Maybe he used refractory cement, who knows. That is the one legitimate gripe I have. It is better to leave the bricks unmortared so you can replace them. But it seems like the oven mason did an OK job to me.
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