The liner sailed from Europe to the US. Probably would have used US style chips and they would have definitely been in US$.
I don't think the chip was from there either, just pointing out there was a 3rd 'S.S. Rex' as you mentioned in another post there were only 2 possibilities.

So yes there is a strong likelihood it is either Santa Monica or LV but I don't believe you could ever prove which one. The thing that bugs me is the denom. $20 doesn't fit with gambling in either location at that time.