Cool designs (courtesy of Nature) in your (what appears to be , to me & my old eyes) flame maple matched-grain veneer table tops , Y. O. !
Since we can't see the cracks you've spoken of , I will add that flame/burled maple grain often has small (repairable) cracks that tend to show up after the wood ages , and is pretty much a characteristic of old (but not always old ... sometimes new veneer has it too!!) wood .
If the cracking (that we're not seeing) does not follow the very 'busy' grain on the tabletop , perhaps it is cracking in the base/core wood that is showing through to the veneer on top .
Inspecting the hardware/joinery that keeps all the parts together would help date your pieces , as in looking for 'recent' manufactured screws , bolts & etc .
Plenty of great marquetry/veneer work has been done on furniture for a few centuries , so the job is finding out what era yours fit into !
Wish I could verify , via your posted images , if yours is antique (100 years or older) or not , but not really enough data to say @ this point .