It showed quite a number of things. Like that there was a pecking order among the dungeons, which was more pronounced among same-type cores. Ittetsu is a beast-type, and so those three, also being beast type, naturally look up to and kowtow to him. It's actually much less clear in the manga now.
Cutting Ittetsu also means the moment where Father asks him the same question he does to the top 10 cores about whether he should make more "children" also got left out. And that leads to yet another cut....Father's supposed to then ask Rokuko the question, singling her out among hundreds of cores, ostensibly because she was standing next to Ittetsu.
And yeah, it's a part of how Rokuko started to get more comfortable being at the gathering knowing she had a friend. It also helped get her more recognition....though being questioned by Father should have done that too. I believe Ittetsu actually mentioned he was defeated out loud in general, and not specifically to those three. So other cores overheard it and started questioning how she did it. In hindsight, I think the author was also trying to plant some hints about how Haku ended up with the traitor moniker herself.
And speaking of Haku, the manga also glossed over the significance of Haku's ranking and in turn the dungeon core hierarchy again. She's Core 89 but she's part of the top 10, which for the most part, is made up of the single digit cores. I would agree all this isn't that important now, but it is later.
I suppose like a lot of adaptations of very popular novels, I've often thought manga versions are meant to be companion pieces, not replacements for the novels. So I guess this is fine? But I still think some of the shock factor of the above cut scenes would have been good for the manga.
