HaKatan- just because there was nothing supernatural doesn’t make it not a neis. Nothing supernatural happened on Purim either, to the untrained eye it was all teva, but we recognized that that was a neis nistar. Mainly because Klal Yisroel were saved from the serious threat of massacre. One can argue the same thing by the Six Day War. The Jewish People (at least those that lived in Eretz Yisroel) were saved from a threat of extermination. G-d saved us through miraculous, arguably hidden, but miraculous nonetheless.
For the record, while I don’t necessarily agree with your views on Zionism, I also don’t view Yom Yerushalayim as a Zionist holiday. I celebrate the victory from a murderous enemy, and the freedom of Yerushalayim from the hands of those who closed it off to Jews. If Yom Yerushalayim happened in the same way with a Goysih army (the UK defeated the Arabs and saved the Jews, they also took control of Jerusalem from the Arabs and gave the Jews access) I would also celebrate it.