I feel bad for the guy who lost out because he didn't understand the rules, but that's not your fault. He didn't purchase the house from you, because the game doesn't allow for that. He paid you to relinquish it, which you did.

That he couldn't buy it then as he'd intended to is a matter of his own character's standing, and something that he should have been in a better position to know than you would be. The requirements for a personal house are that you have to be a Second Lieutenant and that you have to be level 50. The requirements for an FC house is an FC Rank of 6. It's his and not your responsibility to determine whether he met those requirements or not.

It's also not the fault of the other player who ended up buying it when your intended buyer couldn't. He's just someone who found an empty available plot that the game said was available for purchase, so he bought it. He wasn't party to your agreement with the other player, so had no reason to wait for him to resolve the issue. It was kind of him to even consider relinquishing right away. He would have been perfectly justified in saying no, that he'd bought it because he wanted to keep it. But in any case, his relinquishing it wouldn't help anyway, as the other guy would still be in the same boat as when you relinquished it. Until he gets his GC rank up, he can't buy one.

It's an unfortunate situation, but the nearest thing to "fault" that exists here is the buyer's failure to understand the requirements for buying a house. While you might feel bad for him that he had to learn that lesson in such an expensive way, that doesn't obligate you to reimbursing him for the cost of his error.