Does the box regarding taking prizes for KO'ing a Pokémon-ex from the EX-era (like EX Ruby & Sapphire) count as a "Rule Box" for the purpose of Empoleon V's "Emperor's Eyes" Ability?

No, the term Rule Box does not apply to anything prior to Black & White. As of the date of this ruling these things are covered by Rule Box: Pokémon V, Pokémon VMAX, Pokémon-GX, TAG TEAM, Prism Star, Pokémon-EX, Mega Evolution, and Pokémon BREAK (any future cards that may have a Rule Box are also covered.)

Relevant cards

SWSH5_40