Learn Spanish (Latin America): El error decisivo fue sacrificar el alfil. - The decisive error was to sacrifice the bishop.

Even though "was" often translates to era when describing things in the past, fue (the preterite) is used here because the error refers to a specific, completed event—a single bad move in a game. You use the preterite of ser when summing up a completed event or action.

In English I might say "The error was sacrificing the bishop." Can I use sacrificando here?

No, you must use the infinitive sacrificar. In English, we frequently use the "-ing" form as a noun, but Spanish strictly uses the infinitive when a verb acts as a noun or the subject of a sentence. The Spanish gerund (sacrificando) is only used for continuous, in-progress actions.

Doesn't obispo also mean "bishop"? Why use alfil?

They both mean "bishop", but for completely different contexts. El obispo is a religious figure in a church. El alfil is strictly the bishop piece in a game of chess.

Could I put the adjective first and say El decisivo error?

You could, but it changes the tone. Placing a descriptive adjective before the noun in Spanish makes it sound more poetic, dramatic, or subjective. For a factual statement pointing out which specific error cost the game, the standard placement after the noun (el error decisivo) is the natural choice.