Learn Russian: Спорт — мой интерес.

In Russian, the present tense of the verb "to be" (is, am, are) is usually skipped. When linking two nouns together to say that one thing (спорт) is another thing (интерес), you simply use an em dash in place of the missing verb.

Why do we use мой for "my" instead of моя or моё?

Possessive words like "my" must match the gender of the noun they belong to. Because интерес ends in a consonant, it is a masculine noun, so it requires the masculine form мой.

Why don't the endings of спорт and интерес change in this sentence?

Both words are in the nominative case, which is their basic dictionary form. In Russian, when you write a sentence that simply says "Noun A is Noun B", both nouns stay in this basic nominative form.