I have seen that style many times but never in that type of tile that looks like "RacedecK" etc where it just sits on the floor. I have some in my shop but it is only about 1/8" thick and is glued down.
just did a search on "coin" tile. Plenty of results:
I would guess either rubber or vinyl - if they're flexible, asbestos is doubtful, but easy enough to send them off for testing. Truthfully, if they've been down for a while and they're glued, I'd be more concerned about asbestos in the adhesive.
I promise you there is no asbestos in those tiles. Why are you so intent on figuring out exactly the brand of the tile? They look like they've been down there since Clinton was President and you aren't going to get replacements or any trim pieces at this point. Either clean it up and get more use out of it or throw it in a dumpster. Worrying about exactly what it is is pointless.