but what he is giving is just another way of mixing coins, in his own perception.
And we are correctly pointing out what that perception is flawed.
Even although some gambling sites don't collect full KYC as you say, they still keep a complete log of all deposits and all withdrawals, all IP addresses, browser fingerprints, etc. They might not be able to link your coins to your real name, but they can very easily link your deposits to your withdrawals, and link all of that to your IP address and browser fingerprint. In most cases this would be enough for an attacker to de-anonymize you through other means, since most people do not use Tor, have very unique fingerprints, and leave traces of their activity and identity all over the internet.
Even without going through the gambling site at all, since as slaman29 says the vast majority of gambling sites are well known to blockchain analysis companies, watching deposits and withdrawals over a period of time and simply matching timestamps and amounts may even be enough to link your deposits and withdrawals.
I would say that not only is using a gambling site in this way not making your privacy any better, but in many cases it is actively making it worse.