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No that's not a stovepipe and you don't want to be putting another hole in the roof . The exit route should be as short and direct as possible, I would have put a 45 degree right out of the box and another 45 just before going through the division.
If it needed to be directed to the right, it would have been best to direct it up through the cabinets, and build a box around it to conceal it.
PLEASE NOTICE
There is a closed in void above the cupboards and below the ceiling that could easily handle the venting PLUS the size of the venting is what you would use in a commercial kitchen. 4 inch would be lots for a home . 8 inch is overkill. Agree ....easiest route to outside works , even just into the vented roof void...think dryer vent