You know, as much as Dio made introspections about his life and the future in that box, he pretty much will always be stuck on the past.
It is clear not just from scenes like these, where he mentions something of his past, but also from his old plans had he survived revealed in part 6:
Making the future the past, in a way he will always know what will happen. No more surprises, he knows everything that will happen as if it had already happened, good or bad. And, in his eyes, everyone would be glad for that, just like him.
Also.
The way I see it, Danny is more important thing for him than he lets out. Because it is kinda one of the only true victories he trully had against Johnathan.
His father? As much as he tried out-sonning him, Johnathan soon matched him. And Dio could not kill and steal his fortune.
Erina? From his reaction, her cleaning her mouth on the puddle was such a big offense that it undid his victory.
Not only that, he pushed too far and Johnathan's reaction was to not just take it but outright beat him up, something he had been smart enough to avoid much from older people. That beating also undid his victory in the boxing match before.
Even his other victory, stealing Johnathan's body, was only needed out of desperation because Johnathan forced him to cut his own head off, least it burned like the rest of his body.
Danny? It may have been a warning, a retaliation, but it was also the only true victory he had.