Thanks everyone for your replies.
No, I didn't take a screenshot of the first generated address - something wise indeed to do with a sizeable transaction, but it never occurred to me.
When I decided to send another 0.1 transaction, my rationale for it was - if this small transaction also is not credited, then their ETH network is just congested. But unfortunately, a new ETH address was generated as soon as I opened the wallet again.
The new transaction (the one that succeeded), just for reference, is this one:
0x791e76c8f10d6592d17686529349b358a73b7474e39ce5cbdae25b8174971403
Now - could I have made an error? Possible (although unlikely, I obviously copy/paste addresses when making transactions).
But what are the chances that I would randomly select a newly created, valid, never used ETH address?
In any case, I think my request makes sense: YoBit has the private key for the generated addresses, so I'm just asking that they check whether the address I sent the ETH to matches their private key.
But they have never agreed to do that.
Ever tried to contact support friend?
I hope you get your money back.