I think that it goes UNDER the table
CORRECT. THAT HOLDS THROAT PLATE, knobs and sheet metal under table. Sheet metal deflects chips to fall through lower blade housing instead all over your pants, into chip tray below. I'd recommend fabricating a new throat plate, should be full length or a bit more to protrude front edge of table.
Object with handles is part of actual 'pusher'. Uses one of two options; a weighted or hydraulic power feed you can steer in profiling cuts. A #40 or so size chain engages the two sprocket teeth at each side. It works manually as well.
Also likely, your saw has an air pump to blow chips from top of workpiece, via flexible metal line and nozzle.
Unrealized by some, they put bandsawing on the map. Up to then, only sawmills used band equipment, merely to length and resawing,
For my money, no one has handier, better, or more tooling than DoAll, quite extensive. Some no longer available, none difficult to replicate.
For the rest of my money, verticals with a blade welder are unequaled capability in a small footprint, for comparative small investment, perfoming operations no other machine can do, unless modern expensive techniques like wire EDM.