Without doubt, it was a military mistake.
Kitbuqa was a brilliant experienced leader in war, and at the time of this battle, he was over sixty, if not seventy years of age. He was contemporary with Genghis Khan, who died about 34 years before this battle, and Kitbuqa spent all this time in wars and leadership.
As an experienced military leader, he had to leave reserve forces outside the valley, in order to secure the way of return in the event of loss, prevent the Islamic army from encircling the Tatars, and watch any movement of other armies that might come to help the Muslims.
However, this did not take place.

That is indeed the arrangement of the Lord of the Worlds, The Almighty, which goes beyond normal human measures, and forces some people to do particular things under certain circumstances. Had the same circumstances recurred even 1000 times, the man would not have taken the same decision. However, Allaah, the Almighty, wanted to destroy this Tatar army at the hands of the Muslims, thereupon He forced Kitbuqa to make a wrong military decision that neither benefitted his possibilities as an experienced leader, nor his forces as a huge army, nor the battlefield which was like a cage with one gate; and if the army entered the cage and it was closed, there would be almost no way to salvation: {But they plan, and Allaah Plans. And Allaah Is The best of Planners.} [Quran 8:30]
In the great Battle of Badr, we saw how Abu Jahl led his disbelieving army to enter the war after most of his people opposed him, and destruction was the portion of most of the heads of disbelief in Makkah.
We also saw in the famous Battle of Yamaamah, how Musaylamah Al-Kaththaab led his forces to their deaths.
We saw in the Battle of Nahaawand, how Al-Fayroozaan led the Persians to their resting place.
We also saw in the Battle of Al-Yarmook, how Baahaan, the Roman commander, led his armies to the abyss.
It is irrelevant to say here that had the leader thought a little, such-and-such a thing would have happened; and had he deliberated or listened to the advice of so-and-so, the result would have been such-and-such.
My brothers and sisters! They are forced to their death.

No matter how powerful they are, how numerous their armies are, and how varied their war equipment is, in no way could they exceed the Will of Allaah, the Almighty. Verily, Allaah, the Almighty, wants to grant victory to such of His slaves who support Him.
{O you who have believed, if you support Allaah, He Will Support you and Plant firmly your feet.} [Quran 47:7]
It is an authentic unchangeable rule.

Thus, Kitbuqa led his entire army to enter into the valley of ‘Ayn Jaaloot.
In this way, the second part of the Islamic war plan was extraordinarily successful.
Then, the third part of the war plan began, and the start signal came from Qutuz, May Allaah Have mercy upon him.

https://en.islamstory.com/index.php/en/artical/20747/How-did-Kitbuqa-do-that