What exactly counts as Archers?

[DGDobrev]

No. Technically, a unit cannot move/attack more than 2 times per fight. When you give a troop an extra move/attack/etc. they have the right to do that in the end of the sub-turn (as if you gave the same troop the order to wait the first time), after everyone else had moved.

This makes it impossible to have a troop act more than twice per battle. There is a small exception to the rule when 2 demon/executioner stacks start hacking at each other, as they may go on until one of them is destroyed. Another exception to the rule is the Gorguanas, who have a significant chance to get an extra attack if the stack just scored a killing hit. As such, a gorguana can get a lot of moves in one turn as well (limited by the number of enemy stacks currently on the battlefield).

EDIT: I checked the russian guide in an attempt to bring some clarity to the discussion here

If we're talking about Trigger, these are the units he affects:
Skeleton Archer, Archer, Cannoneer, Catapult Goblin, Elf, Hunter, Goblin, Royal Thorn, Thorn Hunter, Alchemist, Repair Droid, Cyclops, Beholder, Evil eyes.

If we're talking about Self-loading crossbow/Arbator it affects:
Skeleton Archer, Archer, Elf, Hunter

If we're talking about the Telescopic sight, these are the units it affects:
Skeleton Archer, Archer, Cannoneer, Catapult Goblin, Elf, Hunter, Goblin.