Casting Righteous Might gives the caster a special attack:
A special attack with a righteous armament version of your favored weapon, which is the only attack you can use. Your attack modifier with the special weapon is +21, and your damage bonus is +8 (or +6 for a ranged attack). If your attack modifier with your deity's favored weapon is higher, you can use it instead. You deal three of your weapon's normal damage dice, or three damage dice of one size larger if your weapon is a simple weapon with a d4 or d6 damage die. The weapon has one of the following properties that matches your deity's alignment: anarchic, axiomatic, holy, unholy. If your deity is true neutral, you instead deal an extra 1d6 precision damage.
The Attack Roll rules seem to make a difference between Strikes and special attacks:
The multiple attack penalty (detailed on page 446) applies to each attack after the first, whether those attacks are Strikes, special attacks like the Grapple action of the Athletics skill, or spell attack rolls.
It not being a Strike would seem to imply that:
Is the special attack granted by Righteous Might a Strike?