The lack of draftstopping/fireblocking is the least of your concern. Yes the chase should have been a closed chase or at least a lid at the ceiling level.

However, if it had been there you would not have found the other problems such as the lack of required clearance from combustibles for the B-vent. Also the blown insulation on the firebox is a fire hazard, both from code standpoint as well as mfg instruction. The insulation in the wall should have been unfaced as the kraft paper will smolder and scorch.

Then there is a question on the vent sizing itself. Is this a "gas log" unit...looks a little shallow from the pic to be a real wood burner? The chimney vent would be too small if the unit is a wood burner.

Sheathing the attic side would generally be acceptable with the proper thimble on the vent at penetration. However there a lot of corrections to be made before recommending closing it up.