The me- prefix is used to form (mostly) transitive verbs, but in this case the base word "minum" is already a transitive verb.
In this sentence, it makes the phrase more formal.

"meminum" = "minum" = "to drink", they're synonyms (see KBBI):

https://kbbi.web.id/minum

meminum/me·mi·num/ v minum;

In everyday speech the me- prefix is usually dropped, especially with these verbs "makan", "minum", "mohon", etc..