Learn Russian: Он никогда не уступает давлению или провокациям. - He never yields to pressure or provocations.

The verb уступать (to yield, give in) requires the Dative case for the thing or person you are yielding to. This is the Dative of Submission you are learning in this lesson: verbs involving submitting, surrendering, or conceding power to an outside force take the Dative.

Can I use уступать for physically giving way to someone, or is it only for abstract things like pressure?

You can absolutely use it physically! A very common everyday phrase is уступать место (to give up one's seat) to someone on the bus. In that case, the person receiving the seat would also be in the Dative case, matching the pattern in this sentence.

Is the double negative in никогда не уступает strictly required?

Yes. In Russian, negative adverbs and pronouns like никогда (never) or никто (nobody) always require the verb to be negated with не. Translating the English structure literally without не would be grammatically incorrect.

Does the conjunction или affect the case of the noun that follows it?

No, или (or) simply links two parallel parts of the sentence together. Because both давлению and провокациям are objects being yielded to, they must both follow the government of уступает and take the Dative case.