Relatively few, but there are some. Most striking to me is the Babur-nama, the memoirs of the founder of the Mughal Empire, Babur. Babur was a Chagetay and Persian speaking of Mongolian lineage, one of the many mirza, princes descended from the great Khans; he was a fifth generation descendant of Timur (aka "Tamerlane") and a fifteenth generation descendant of Genghis Khan.

There are not too many other works written by rulers like his Babur nama. It is personal and idiosyncratic, he's a poet as well as an empire builder, he gives us a picture of his own character -- a self serving one no doubt, but a psychologically nuanced one, not just fluff-- that is remarkably different. Later Mughal emperors have their stories told in documents like the Akhbar-nama, but these are far less interesting, written by sycophantic courtiers and largely without any sense of the person.

Babur really seems to want to talk to us, the reader, across time, he tells us directl

What I have said is all fact. I do not intend to aggrandize myself with what I have written. What I have written is the truth.

As the scholar Stephen Frederic Dale says of Babur and the Baburnama

In the Baburnama and in his poetry, Babur distinguished himself as an exceptional figure in premodern (or pre-colonial) Islamic literature, by vividly conveying a sense of himself as a unique personality. Indeed, he wrote so directly, so openly, and so extensively of himself that it is possible to say that he represents for Islamic civilization what his Italian contemporary Benvenuto Cellini represents for European civilization: the most completely revealed individual of the 16th century.

Babur gives us a kind of reflection on his own decisions that's really hard to find in other pre-modern writing, criticizing his own decision to treat prisoners harshly, Babur says

In truth this seemed to be reasonable; our men were ordered to take what they knew to be theirs. Reasonable and just though the order was, [I now] understand that it was a little hasty.... In conquest and government, though many things may have an outward appearance of reason and justice, yet 100,000 reflections are right and necessary as to the bearings of each one of them. From this single incautious order of ours, what troubles! What rebellions arose

Babur does not strike me as "lonely". He takes pleasure in military exploits, in his comrades in arms, in poetry. To hear him tell it, he's a happy guy. He tells us of his worries, and gives us this picture of his poverty in Tashkent

During my stay in Tashkent, I endured much poverty and humiliation. I had no country or hope of one! Most of my retainers dispersed; those who remained were unable to move about with me because of their destitution. If I went to my uncle The Khan's gate, I went sometimes with one man, sometimes with two. It was well he was no stranger but one of my own blood. After showing myself in his presence, I used to go to Shah Begim's, entering her house bareheaded and barefoot just as if it were my own.

This uncertainty and want of house and home drove me at last to despair. I thought, 'It would be better to go off by myself than live in such misery; better to go as far as my feet can carry me than for others to see me in such poverty and humiliation. Having settled on going to China, I resolved to head off on my own. From my childhood up I had wished to visit China but had not been able to manage it because of the responsibilities of ruling and other obligations. Now sovereignty itself was gone, and my mother, for her part, was re-united with her (step)-mother and her younger brother. The hindrances to my journey had been removed; my anxiety for my mother was dispelled.... Once in Moghulistan and Turfan my reins would be in my own hands, without check or anxiety. I confided my scheme in no one. Why not? Because it was impossible for me to mention such a scheme to my mother, and also because it was with other expectations of me that my few companions in exile and privation had sacrificed all for me and endured a like change of fortune. To speak to them of such a scheme would be no pleasure either....

That's a lot of "interior life", a man describing what he thought and did, what he concealed of his intentions and why-- a very modern and psychological portrayal. Indeed, if I were to randomly come upon the Baburnama and not know its provenance, I would have imagined that it was a modern fiction, like Memoirs of Hadrian or I, Claudius.

In terms of other works by rulers-- the Meditations of Marcus Aurelius comes to mind; it's not an autobiography, but it is a personal and psychological work

Elizabeth I of England never wrote anything like an autobiography, but her letters and speeches are filled with surprising insight and psychological realism. Korean King Sejong I ("the great") wrote quite a bit, but never an autobiography.

See:

Dale, Stephen Frederic. “Steppe Humanism: The Autobiographical Writings of Zahir Al-Din Muhammad Babur, 1483-1530.” International Journal of Middle East Studies, vol. 22, no. 1, 1990, pp. 37–58.Dale, Stephen F. “The Poetry and Autobiography of the Bâbur-Nâma.” The Journal of Asian Studies, vol. 55, no. 3, 1996, pp. 635–664.

Thackston, W.M (translator) "The Baburnama: Memoirs of Babur, Prince and Emperor" (Smithsonian:1996) [note, there are several translations of the Baburnama, personally I find the Thackston the easiest going]