Epictetus was a stoic. Stoics as a general characterization have little regard for abstract metaphysical speculation about the nature of personhood and the divine. As a student of human nature, his topics are primarily about choices humans can make for the good life. Stoics tend to characterize divinity as the source of that which cannot be controlled and must be endured. Stoic thought such as that of Epictetus is more concerned with introspection and the regulation of worldly life, which is a very objective domain of discourse to the Stoic.
Let us open with a quotation in Wikipedia's article attributed to Epictetus ultimately:
The emotions of grief, pity, and even affection are well-known disturbers of the soul. Grief is the most offensive; Epictetus considered the suffering of grief an act of evil. It is a willful act, going against the will of God to have all men share happiness.
But the ultimate is an important caveat because it brings about a frequent challenge when talking about philosophers from Antiquity. From the same article:
No writings by Epictetus are known.
Thus, what Epictetus did and didn't believe is to some extent a question of what the interpretation of others in Antiquity believed themselves. Historians, however, do have a historical interpretation of Epictetus that can help us draw conclusions. The Enchiridion (Google Books)(Gutenberg Project)(WP), for instance, was derived from the Discourses of Epictetus. And from the Enchiridion article:
Eschewing metaphysics, Arrian focuses his attention on Epictetus's work applying philosophy to daily life. The book is thus a manual to show the way to achieve mental freedom and happiness in all circumstances.
From Gutenberg's Enchiridion:
Remember that you are an actor in a drama of such sort as the Author chooses—if short, then in a short one; if long,  then in a long one. If it be his pleasure that you should enact a poor man, or a cripple, or a ruler, or a private citizen, see that you act it well. For this is your business—to act well the given part, but to choose it belongs to another.
This is of course, was written by a man who had been a slave and then worked his way to freedom and entrusted with the care of the wealthy. The nature of personhood therefore was one of quite the practical import to him directly. In your quotation, it is likely that Epictetus would have been metaphorically comparing self-knowledge and self-control to literal freedom, and the opposite to slavery. Epictetus, like many contemporaries, believed that there was a practical, inescapable worldly existence and was concerned with self-knowledge and the practical, realist implications that the knowledge brought. It's hard to imagine anyone who being subjected to the potential penalties a slave could be subjected to rejecting objective reality.
The other portion of your question addresses whether or not Epictetus would consider the divine because unlike the Scholastics, he was more interested in practically worldly experience and decisions than metaphysical speculation about divinity. As such, Epictetus saw divinity as the source of that which one cannot control. Thus, a reasonable interpretation is that whether God or gods were at play, it one would be better off attending to the here and now than engaging in frivolous discourse about the nature of things not clearly understood or of little pragmatic value.
According to this source, Epictetus had specific thoughts about choices and the gods in terms of virtue:
When some one [sic] asked, How may a man eat acceptably to the gods, he answered: If he can eat justly and contentedly, and with equanimity, and temperately, and orderly, will it not be also acceptable to the gods? But when you have asked for warm water and the slave has not heard, or if he did hear has brought only tepid water, or he is not even found to be in the house, then not to be vexed or to burst with passion, is not this acceptable to the gods? How then shall a man endure such persons as this slave? Slave yourself, will you not bear with your own brother, who has Zeus for his progenitor, and is like a son from the same seeds and of the same descent from above? But if you have been put in any such higher place, will you immediately make yourself a tyrant? Will you not remember who you are, and whom you rule? That they are kinsmen, that they are brethren by nature, that they are the offspring of Zeus? But I have purchased them, and they have not purchased me. Do you see in what direction you are looking, that it is towards the earth, towards the pit, that it is towards these wretched laws of dead men? but towards the laws of the gods you are not looking.
If this quotation is true to the actual Epictetus, then we have by implication that he didn't regard men and the gods so different as a person to not consider them sharing qualities with people, but still clearly recognizing their divinity. For contemporary Christians and within the Judeo-Christian mythos, God is seen as substantially less human than the Polytheistics Greeks understood their gods. Among psychologists, this difference in interpretation can be understood as differences in degree of anthropomorphization.