What part of speech is 'closer' functioning as in 'I moved closer'?

'I moved closer.'

At face value, 'closer' seems to be acting like an adjective; however, I don't see anything in the sentence to which it can refer. A friend suggested that 'to move closer', 'to move further', and friends are a family of phrasal verbs, but this seems like a cop out to me.

I think the most likely answer is that 'closer' is functioning as a comparative adverb. A very common error in colloquial English is to use an adjective in place of the adverbial form ('I am doing good' instead of 'I am doing well'). Correcting for this error yields 'I moved more closely'. Admittedly, this sounds awkward, but I think that has more to do with the uncommon phrasing than the technical integrity of the expression.

Is there something I am missing here?

Closer in this sentence is the comparative of the adverb close.

close (adv.)

at or to a short distance or time away

[M-W]