Learn Turkish: Kendisi bir gurme olarak, bu kasabaya has o yemeği hiç tatmamış. - As a gourmet himself, he has never tasted that dish exclusive to this town.

Has means "exclusive to" or "typical of". It always pairs with a preceding word in the dative case (the -(y)a / -(y)e ending). Here, kasaba (town) takes the dative suffix to become kasabaya. You could absolutely replace it with özgü or mahsus (bu kasabaya özgü or bu kasabaya mahsus) with no change in meaning.

Why is bu kasabaya has placed right before o yemeği?

In Turkish, modifying phrases come directly before the noun they describe. The entire phrase bu kasabaya has acts like a long adjective meaning "exclusive-to-this-town". It describes o yemeği (that dish), so it must sit right in front of it.

Why does the sentence start with kendisi instead of the standard pronoun o (he/she)?

Kendisi literally means "himself" or "herself". While o would be grammatically correct, using kendisi adds emphasis to highlight the irony. It stresses that he himself—despite being a gourmet—has missed out on this local dish.

Why is the verb tatmamış using the -mış past tense rather than the definite past tense tatmadı?