Learn German: Wir spielen das Gambit, denn dieser Schachzug gilt als aggressiv. - We play the gambit because this chess move is considered aggressive.

The word denn means "because", but it is a coordinating conjunction. This means it occupies "position 0" and doesn't change the standard word order of the clause that follows it. Therefore, the subject (dieser Schachzug) is in position 1 and the verb (gilt) is in position 2. If you used weil instead, the verb would indeed go to the end: ... weil dieser Schachzug als aggressiv gilt.

Why doesn't the adjective aggressiv take an ending here?

In this sentence, aggressiv acts as a predicate adjective describing the subject (dieser Schachzug). The phrase gelten als (to be considered as) functions similarly to the verb sein (to be). Just as you would say der Schachzug ist aggressiv without an ending, you say er gilt als aggressiv. The adjective remains uninflected.

If I wanted to say "is considered an aggressive move" instead of just "aggressive", what case would the noun phrase take?

It would take the nominative case. Because gelten als acts like an equals sign linking the subject back to itself (a copula verb), both sides of the equation are nominative. You would say: ... denn dieser Schachzug gilt als ein aggressiver Zug.

What is the infinitive of gilt and how does its meaning change when paired with als?