Learn German: Dieses Gambit erweist sich als ein brillanter Plan. - This gambit turns out to be a brilliant plan.

Even though there is a reflexive pronoun (sich), the verb phrase sich erweisen als acts as a copula. This means it links the subject (Dieses Gambit) to a description of that subject. Because both parts refer to the same thing, the noun phrase after als matches the subject's case, which is the nominative.

What is the exact difference in meaning between using sich erweisen als and simply using the verb sein?

While sein simply means to be, sich erweisen als means to turn out to be or to prove to be. It emphasizes that the true nature of the gambit was revealed over time or through its execution, rather than just stating a static fact.

Why does the adjective brillanter end in -er in this sentence?

Plan is a masculine noun in the nominative case. Because the indefinite article ein has no distinct ending here to indicate the masculine gender, the adjective has to do the heavy lifting. It takes the strong ending -er to clearly signal that the noun is masculine.

Could I drop the noun and just say the gambit turns out to be brilliant?

Yes, you can use an adjective on its own by saying Dieses Gambit erweist sich als brillant. Notice that when an adjective is used after als without a noun following it, it is not inflected and takes no declension endings.