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I am 95% sure that Coinplay is being operated by the 1x group. While the brand is pretty new, they might try to keep it clean.
I was about to start testing this casino, but right now I decided to skip it. They are changing the T&C on the go, trying to hide the connection with the 1xbit brand, which is already a red flag to me.
I think you are right. Besides the similarities you found, from what I can tell, it's clear that both websites were generated by the same software. The fact that they have identical HTML coding is a strong indication that they were created by the same person. And this is important because it shows that the owner of this site is likely someone who has been involved with 1xBit/1xBet.
For more evidence of this, check out the HTML code on each page:

Moreover, both websites share a main CSS file with identical code.
https://coinplay.partners/public/styles.1542de2bccf502eda2a6.css
https://partners1xbit.com/public/styles.1542de2bccf502eda2a6.css
The same CSS is also used by "1xpartners.com"
https://1xpartners.com/public/styles.1542de2bccf502eda2a6.css
I think it is safe to say that they were created by the same people. In fact, I believe that the two websites are part of an entire network, namely 1xpartners.com, that are all connected.