There is nothing incorrect or ungrammatical about the sentence:
because this is different from saying:
「私が世界で一番偉いだ。」, which is ungrammatical.
「だって」 in the sentence in question is placed after a quote, is it not?
Depending on the context, it may be:
This 「だって」 expresses one's surprise, criticism, etc. toward the statement that is being quoted. The fact that the quoted statement happens to end in an i-adjective has no effect on the validity of 「だって」.
Since that is a valid usage, you can find it in dictionaries, too. (Not sure about bilingual dictionaries as I almost never use them.)
See definition 三 here:
「私が世界で一番偉いか？？」 feels very different because it is a plain yes-no question and it does not express the surprise or criticism that I mentioned above which 「だって」 as a sentence-ender expresses.
I think I should mention this before I go. This 「だって」 is pronounced VERY differently than 「だって」 that means "because" as in 「だって女の子だもん！」.