Talking about someone’s character and saying someone “is a character” are two very different things, in different registers.
Commented Jun 4, 2019 at 20:52The Oxford English Dictionary (character, n.) reports this definition along with several examples. The two earliest ones suggest the usage came about in the late 18th and early 19th centuries.
The distinguishing feature is that the person is extraordinary, or that they stand out due to some oddity, eccentricity, or (to go by your definition) entertainment value.
This usage likely comes from the more generic sense of someone's character as personality and moral quality. Again from the OED:
9.a.The sum of the moral and mental qualities which distinguish an individual or a people, viewed as a homogeneous whole; a person's or group's individuality deriving from environment, culture, experience, etc.; mental or moral constitution, personality.
1666 H. Bennet Let. 9 Feb. in Lett. Earl of Arlington to Sir William Temple (1701) 60 Tho he had Opiniastred the Point, as restily as became his Character, yet we are perswaded that..he is not dissatisfied.
1726 Bp. J. Butler 15 Serm. xii. 234 There is greater Variety of Parts in what we call a Character, than there are Features in a Face.
These and similar personal meanings for character (including the name of a person portrayed on stage by an actor) became popular in the 17th century. They are all figurative uses originating from the sense of character as mark, letter (today seen in uses like the number of characters in a text field), or imprint. The first documented figurative use referred to the imprint left by baptism upon one's soul:
To sum up, character began as a kind of mark or imprint, then was used to describe how a soul or spirit was marked, then was generalized to personality or moral quality in general, and thence applied to people and especially to remarkable or extraordinary people.