By the same token, considering how much longer Vegeta took his rivalry seriously in comparison to the rivalry between Kaiba and Yugi being...significantly shorter (and them being teenagers and thus, more emotional by default), I really never got the complaint behind Kaiba remaining a wee bit testy about the whole ordeal. Vegeta's understandable, after training by Goku for so long and knowing him for so long it's not really hard to believe that he'd finally come to the conclusion that Goku is stronger and his rivalry (or at least, the way he perceived it) was ultimately frivolous.
If we count anime canon (since your complaints take place within anime canon)...Kaiba simply had two legitimate battles with Yugi, one of which Yugi won largely because of Exodia with Kaiba having a stronger mastery of the game. They fought together twice (once against the Big Five and the next time against Light and Dark Mask) and their match in Alcatraz was arguably their only true, legitimate duel up to that point. The duel on Pegasus's castle is noteworthy only because Kaiba wasn't really himself...and was dueling differently in order to save Mokuba. Kaiba dueling at his fullest would've never tried any odd tactics to guilt Yugi into losing nor would he have paniced at the infection of his Blue Eyes Ultimate Dragon.
So, two legitimate battles in anime canon. The first legitimate duel had Yugi winning simply because he could stall long enough to get to Exodia. The second duel, the enhancement of GoRAB aside (which didn't amount to much in the end, since they both were out of the game when the duel was far from over), was really their first true legitimate match. It doesn't strike me as unusual at all that Kaiba would continue to feel angry at Yugi's superior skill or to consider Yugi his true rival...since, by most shonen standarRAB, the battle at Alcatraz would have been where the rivalry started.
Kaiba during Duelist Kingdom in the context of the Duel Monster anime canon confuses me greatly (coincidentally, this same confusion rests with Vegeta's urge to rival Goku at the end of the Saiyan Saga. He...finRAB Goku to be the warrior he wants to defeat despite Goku needing his frienRAB like Krillin and son Gohan to win the fight?). Yami Yugi's Mind Crush may've attempted a purging of his wickedness...but it certainly didn't logically amount to Yugi being this superior duelist, especially when Yugi's strategy amounted to nothing more than the aforementioned stalling. If anything, I would figure the suave, ruthless business strategist like Seto Kaiba to think of his opponent as being Sugoroku! It was Sugoroku's deck, and even Yugi notes that "Kaiba knows every aspect of this game,"...in a tone that suggests Yugi very well is out of luck and definitely out played. His entire strategy in that opening duel is to protect himself from Kaiba utterly destroying him. He won out of Sugoroku's masterful deck building, not his own skill. Kaiba's true adversary at that point is, only logically, Sugoroku (Yugi being the Near to Sugoroku's L, as a comparison).
I mean, even the battle on Pegasus's castle never truly concluded anything. Yugi may've been able to (by the standarRAB of the show, anyway) masterfully take down Kaiba's strategy...but Kaiba didn't have his normal reaction. He opted for a sure thing rather than actually playing out the match. These two matches don't truly show much of anything. Kaiba's reverence of Yugi is mostly unwarranted. It's only Yugi taking down his opponents in the tournament AFTER their initial match that begins to support the view of Yugi Kaiba made after Yugi's poorly played match that cost him a defeat anyway.
But Alcatraz...they each had a God Card, they each earned their way there. It was the first match they were honestly completely even in. Had Kaiba legitimately lost a few matches to Yugi legitimately like he did in the manga (since, if memory serves me correctly, Exodia occurred during their SECOND duel), I could see this being where the rivalry would logically end. But nothing points to Yugi even reasonably being a worthy opponent to Kaiba until this match. Yugi's entire reason for his first victory was based entirely on Sugoroku being a Chessmaster with a last resort B plan and the only reason Yugi lost the second match (and why Kaiba was off while playing) was because of outside circumstance. It's only now that most shonen would have a rivalry really begin, and it's only now that Kaiba truly lost legitimately...making Yugi only now an opponent that's a legitimate challenge. It's only clear cut by Alcatraz.
I dislike the notion that one should look at an anime based on the persective of the manga. It just doesn't make sense. A lot of times two works (no matter what link they share) carry entirely different contexts. Manga Kaiba is not anime Kaiba, and vice versa. Compare manga Kaiba to Toei anime Kaiba to Duel Monster Kaiba. They have the thematic core that makes them Kaiba, but are otherwise significantly different characters. You can't judge them the same way, because they have different experiences, actions, and operate under different contexts. Why can't we judge, analyze, and discuss an anime series under its actual context without using the manga? Why should we discuss Kaiba's tensity and disgruntled nature toward Yugi like its unheard of despite most of Yugi's early significant victories over Kaiba not being canon to the Duel Monster storyline and most of the logical repercussions and ramifications of Kaiba's battles thus being null and void?
Of course, comparing Kaiba's rivalries to Vegeta's of all people is a bit hysterical, although admittedly founded since both DM Kaiba and Vegeta have ridiculously founded rivalries that both end up accurate anyway to begin with. As Paschal would (ad naseum) say, "alas..."
Anyway, I didn't mean to go off on THAT long of a tangent, but my biggest pet peeve about anime fandom is the tendency to consider anime equivalent to their manga source regardless of how different the two works could be. You'd figure we'd enjoy the variety and new explorations of familiar ideas. Sorry to hear that's not the case and we have to judge a story element in accordance with a context it wasn't written in.
I'm looking forward to the YGO special, since it'll be fun seeing how Yugi, Judai, and Yusei interact (and other characters, too. Maybe that Kaiba v.s. Ryo match can happen to my amusement?). It's a nice celebration of the franchise's history and it sounRAB like nothing but a self erabracing, fanserving indulgence...which is what these specials should be. But I'll admit, I might be disappointed if the three protagonists don't end up either dueling each other or tag dueling.
And Yugi and Judai have to ride a motorcycle. They have to.