I suspected that is what it was but was not sure. Otto Has explained. So no, it's not structural. He also has a point about just using it. Anyway, assuming you do want a wind up spare carrier, take that original one off and keep it on a shelf for now. Leave any brackets that don't interfere with the new hoisted tire.
The view below shows you the crossmembers. They are usually riveted and are structural (beefy'ish). They can be used to support a spare winch. or You can add a piece across the frame rails like a "new" crossmember and bolt it to the rails. or You can add a piece running parallel to frame rails, in the middle, to suppoprt the winch. Just study how they suppoted the origional hanger to see what was acceptable size metal, bolt sizes, support and general strength. You can ask here what we think of your proposed structural idea if you wish. You don't need to go overboard with structure.
Obviously a tire fits under there. I should have said that. But you still need to see where it will 'nest" best. Find a spot you like so tire gets cranked up tight and level and see where that nesting locates the winch. The "tight" comment is to point out a possible difference in design approach with the original vs hoist methods.
The ones I've done made life a lot easier and are not hard to do. You really don't have to lay down, kneel down or get dirty if you don't want to or can't.... to retrieve or load a spare.
Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn