Done my fair share of vent hoods ... Usually, the vent can be directed either upward, out the back or toward the front (which blows, not vents).
My first instinct is to cut out the wall and reframe to center the hole. No big deal with some 2x4s and some drywall fixing. However, if that is a bit too scary ...
You problem is that the hood needs to sit flush with the back wall. You have no choice here. This aligns the front bolts which come down through the upper wood cabinet. If you hold the hood off the back wall, those bolts will NOT catch the threaded holes in the hood ... MAJOR OOOOOPS.
So, your next best solution is to vent upwards through the wood cabinet. That might entail cutting into the drywall above the cabinet and then diverting at 90 degrees to the outside wall (my guess is you have a 2nd story above your kitchen?) Again, no big deal because you can replace the drywall and re-paint inside the cabinet.
FIRST, I would take this up with the vent hood manufacturer. Just identify the model and style you like BUT DON'T BUY IT. Write down the model number. Call the manufacturer and send them the pic. They should have something that can help.