Learn Polish: Mój przeciwnik oszukiwał w dwóch grach.

It is in the Locative case, triggered by the preposition w (in). The Locative form of the number 2 is dwóch for all genders. So, even though gra (game) is feminine and would be dwie gry in the Nominative, the number takes the universal Locative form dwóch here.

Don't numbers usually force the noun into the Genitive case? Why is it grach (Locative plural) instead of the Genitive?

That rule only applies when the number is in the Nominative or Accusative case. When a sentence requires an oblique case like the Locative (here, because of the preposition w), small numbers like 2, 3, and 4 just act like adjectives. They simply match the case of the noun. Since w requires the Locative, both the number and the noun take the Locative plural: w dwóch grach.

Why use the imperfective verb oszukiwał instead of the perfective oszukał?

The imperfective oszukiwał emphasizes the ongoing or repeated action—he was actively cheating during those games. If you used the perfective oszukał, it would mean he successfully tricked or deceived you as a single, completed event (for example, tricking you into giving him money).

Is there a trick to remembering the word przeciwnik (opponent)?