You seem to lack an understanding of how share structures and corporate governance works. That’s ok, it’s not common knowledge and I hope I don’t sound condescending.
Treasury shares are not used for voting. Because technically, all the assets (cash, shares etc) belong to shareholders. All shareholders in aggregate represent Nintendo and the board exists to serve those shareholders. The board members cannot use the treasury shares for themselves. Board members can vote to recommend deals and other motions but it’s shareholders who get the final vote on any major corporate governance.
If you want to know why Nintendo bought back shares. It had nothing to do with control. Buybacks are done to reduce free float and increase share price.
Do you understand now why the treasury shares are irrelevant for the purpose of voting?
Nintendo is insulated from hostile foreign acquirers thanks to the Japanese government but the board is obligated to consider all serious offers, which is why they declined to include anti takeover provisions during their latest board meeting.
https://www.nintendo.co.jp/ir/en/management/governance.html
Edit: no more comments from me on this topic.