Kaiba allows it because the investor owns Industrial Illusions, and distributes the game that had gotten him through a great deal of hardship. Pegasus knows that just as well as he does, and it's what binds their companies together.

Yuugi might not understand the breadth of it, and that's fine. Pegasus won't stop calling him "Kaiba boy" though. Just an odd little parlance, a mixture of English and Japanese that doesn't quite translate well, but then, there's more than just that in the way he speaks. English words are mixed in here and there, and Yuugi can probably parse them!

So Pegasus won't alter his speaking pattern. In fact, he holds a hand out to shake, hoping that Yuugi would take it as warmly as it was offered.

My, but his heart sings for the elder Kaiba, doesn't it? How intriguing! No one blushes like that for nothing!

"I think you'll be one of his finest acquisitions," Pegasus says kindly. "And speaking of him, it's time for my meeting! Would you like to join us? I know you must have a lot of work to do, but I'm sure you wouldn't mind indulging me, just a little? I would love to tell him of how courteous you were!"