Seto Kaiba is an incredibly complex character and from your prologue I'm fairly sure that you know that. As a result, writing specifically from his perspective is incredibly difficult and you have a bit of my respect just for attempting it.
But I felt like he was a little OOC here. You had him thinking 'Cool' twice and it's a word that doesn't quite suit him. He's intelligent and he's got a rather immense vocabulary. I'm sure he'd use it.
Also, I don't think there's any chance that Seto Kaiba would ever smile reassuringly at anyone. He didn't smile once during the entire series (he kind of half smiled when he got his brother back from Pegasus, which should say something). The idea of a reassuring smile on his face is a little frightening to me. Almost like he'd completely snapped.
I hope this doesn't come off too harsh, those were simply two rather large details that I wanted to point out. Kaiba's complex and that gives writers some elbow room but only within reason. He's simply not a friendly person no matter how you slice it. Hopefully it'll help out for your future chapters. =D