Learn Finnish: Nainen, jolla oli tällainen chili, voitti. - The woman who had this kind of chili won.

Tämä means "this" (pointing to a specific chili), while tällainen means "this kind of" or "such a". It describes the quality or type of the chili rather than identifying one specific chili.

Why is the relative pronoun joka (who) written as jolla in this sentence?

In Finnish, you express "having" something with the adessive case (-lla / -llä) plus the verb olla (to be). To say "who had", you must put the relative pronoun joka into the adessive case, becoming jolla (literally "on whom was").

Why is tällainen chili in the basic nominative form here?

In a Finnish "to have" sentence, the thing being owned is actually the grammatical subject. Because a chili is a whole, countable object acting as the subject of oli, both the noun chili and its describing adjective tällainen stay in the basic nominative form.

The verb at the end is voitti. What is its dictionary form, and why does it keep the strong -tt-?

The dictionary form is voittaa (to win). This is the past tense for "she won". Due to consonant gradation, the double -tt- weakens to a single -t- in closed syllables like voitin (I won), but it stays strong in voitti because the third-person singular ending leaves the syllable open.