A Superiority Attitude? (Note that the following is not in any way intended to judge any ill intent by the OP. It is only an observation that certain language forms can be received in an emotionally negative way by readers.) I might caution that your enthusiasm regarding "incorrect grammar" and "uneducated speaker" may appear to many readers to be similar to a narrow "Standard Educational English is right and a" condescending attitude. The editorializing statements and inflections may also appear to be similar to passive-aggressive troll-like language behavior rather than a sincere question about the motivations behind the grammar used in a song.
Astonishing? Not! It's far from astonishing to find non-standard, informal, or common vernacular in popular American songs. In fact, it's quite common. What might be astonishing is that you waited until "she don't know you" to be astonished. That's deep into the second verse, even after "but you still ain't calling", "you must not-a got 'em", and other gems of a certain recognizable dialect.
Confused Quesiton: To suggest a binary choice that "it's intentional or the speaker is uneducated" is a confusion of levels. The "intention" of creating a character that uses a particular dialect must be attributed to the writers of the song. The "speaker" is the fictional character "Stan" depicted within the song. To question whether a fictional character ("Stan") is "uneducated" might be totally moot in the respect that he is fictional. The next section deals with this further.
Educational Level of the Character Stan: Any "backstory" of a fictional character could be filled in with any sort of creative story desired. Perhaps he was a Rhode Scholar that became disenchanted and suffered schizophrenia and obsessive-compulsive behavior, denounced his education and returned to his roots, re-adopting the language of his original culture. This possibility does have historical support. But it's just absurd conjecture about the history of a fictional fantasy. However, suppose we indulge ourselves with some plausible realistic perspective -- it still raises the question, "what kind of education and how much?" Some would support the notion that people are not "educated vs. not-educated". They are educated to various degrees along various dimensions. Stan certainly has a penchant for communicating his ideas clearly and succinctly. And that seems more educated than many high school (dare I say even college) graduates.
Educational Level of Writers: It's notable that Stan by Eminem is a highly successful, acclaimed, and popular hit single. The credits indicate the song was written by Dido Armstrong, Paul Herman, and Marshall Mathers. The success of this song is certainly based on a large team of highly talented and educated artists and professionals.
Correct English? There is no single official standard for correct English grammar. Songs often use common vernacular dialects of English. A common vernacular dialect is only "incorrect" as someone's judgement relative to some other dialect, typically certain standardized dialects such as self-appointed style guides and educational materials. Standard English is itself a dialect, and there are many "Standard English" dialects.
what is the purpose of this non-standard language: To say it's an "intentional misuse of language" is missing the point. It's better characterized as an "intentional use of a popular dialect" that would prove to resonate with those who understand that dialect and directly or indirectly relate (positively or negatively) to the character Stan.
How it appears to the native English speakers? The non-standard English use in the lyrics sounds perfectly in-line with what people understand to be some standard regional or socio-economic dialects. In fact, it's not too far linguistically from your own language; In your following sentence, I've highlighted elements in bold that are similar to some common vernacular English dialects rather than formal Standard English.: "First I didn't believe my ears, but when I read out the lyrics I got astonished."