"She never once tried to entrap someone."
"And yet, never once did she try to get back at those who deceived her."
Untrue and untrue. Kanzaki Nao has used trickery, lies, manipulation, and careful planning (e.g. trying to get close to Abe in order to derail the Hasimoto group in two games in a row) on multiple occasions to ensure her / her group's victory. Akiyama has employed even more brazen strategies on her behalf.
As for trying to get back at others, she has definitely shown anger and vindictiveness towards many who have just been trying to play the game. She has particularly sought to get back at Yokoya and has said she wants to see him lose out on his winnings. I believe she may have made some lesser comments about a couple others as well.
"If there's one person who would never ever betray them, it's Kanzaki Nao."
Yeah, unless it suits her purpose.
If I was not so close to the end, I would drop this manga.