is it ok to use pure tung oil if I don't know what the original finish was?
The short answer is no.
There are some finishes that it would be OK to apply tung oil to1, but with commercial factory furniture it's extremely unlikely any such finish was used.
So instead you're faced with some amount of remaining commercial finish, either lacquer2 or conversion varnish. No oil should be applied to either of these, even if you wanted to use an oil for a table (which is questionable, because tables really require more protection than straight oils can provide, even tung oil).
What instead
There's likely to be some amount of the original finish still present in or on the wood (except in areas where it has been worn down to bare wood and there appears to be a lot of edge wear here from heavy use or excessive cleaning).
So if you don't want to strip back to begin again with bare wood the viable options are wax, or a harder finish.
Wax can be used because waxes can go on top of anything.
Finishes that dry hard can be applied to other hard finishes, as well as bare wood, and even if they don't bond to the previous finish chemically they can grip to the surface well enough for practical purposes. They then cure hard enough that the surface isn't permanently gummy or sticky.
See previous Answer for more details on surface prep.
1Basically, any straight oil or simple oil finish.
2Now multiple kinds, although formerly it was 100% nitrocellulose.