I'll toss my hat into the ring with an opinion that your little item is indeed a "replicantique-ish" item .
Unless my eyes are wrong , the image of the screwhead is of a type known/aka 'squaredrive' & 'trailerhead' , which are pretty modern screws .
Something about the whole assembly of the item screams "airtools" to me .
General design of your side table reminds me of many 6-legged lamp/parlor tables seen in homes along the Mississippi , when steamers worked the big muddy .
Sadly enough , I'd say yours is not from that century !
It would however , be a pain to repair the veneer (unless you've got a stock of it & a press) , but @ least it would be a practice piece , until a 'real one' (antique) comes along !
You could also 'shabby chic' (distress/paint/ect) it up with some faux painting , after removing the veneer top .... have seen some faux painters that are amazingly artistic ...
Might have been used as side-tables for a low , "cruise & swing" , riverboat-themed type sofa/waterbed ?(
The story of using veneer woods goes back centuries & centuries + some , to the way-old-timey-time , Ellenshar , sometimes known as 'inlay' , 'overlaid' , 'marquetry' (etc) woodworking/artistry .
Folks looking for 'solid wood' furniture (vs laminates/chipboard) would have been the original 'target' customers for these 'furniture-store' items , IMO .
Sometimes these heavy-looking items are @ least sturdy , other times , not too much .