For Magery, Necro, Mysticism, and SW it does, but only slightly. For players, every 10 INT increases spell damage by 1%. It's nowhere near that for pets. A 1,030 INT Serpentine Dragon isn't doing 33% more spell damage than a 700 INT WW, even with Magery/Eval being the same. Initially, INT didn't affect pet spell damage AT ALL, until i talked to either Bleak or Kyronix about it on TC during Pub 97 testing. Now it only slightly affects pet spell damage.
But yeah, STR (and melee) contributes far more to a pet's damage output than INT (or most spells other than EoO) do. Even a Serpentine Dragon with 1,030 INT/1,500 Mana/30 MR/120 Magery/120 Eval/120 Med/120 Focus and Magery Mastery can't compete damage wise with your typical 700 STR Chiv+AI pet. Not even close. ESPECIALLY once they run low on Mana (which happens even with the afore-mentioned Serpentine Dragon Archmage).
INT does boost passive mana regeneration rate as well, which is why we suggest bumping it to 370 on pets with 700 STR/150 DEX.
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Also Int only works for Magery SDI.