Does First Strike apply when two creatures fight, i.e when they have been targets of the Fight ability?


No. First strike only works in combat, and Fight is not a combat ability. See the Comprehensive Rules:

701.12. Fight

701.12a A spell or ability may instruct a creature to fight another creature or it may instruct two creatures to fight each other. Each of those creatures deals damage equal to its power to the other creature.

701.12b If a creature instructed to fight is no longer on the battlefield or is no longer a creature, no damage is dealt. If a creature is an illegal target for a resolving spell or ability that instructs it to fight, no damage is dealt.

701.12c If a creature fights itself, it deals damage to itself equal to twice its power.

701.12d The damage dealt when a creature fights isn’t combat damage.

702.7. First Strike

702.7a First strike is a static ability that modifies the rules for the combat damage step. (See rule 510, “Combat Damage Step.”)

  • And even if first strike did matter, the damage would still be dealt during a single resolution, and creatures don't have an opportunity to die from lethal damage until after the spell has resolved. I can't imagine there are many edges case where it matters whether the damage is dealt simultaneously or one after the other.
    – Arthur
    Dec 21 '18 at 9:34

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