On my installation of Baldur's Gate: EE (both with Seige of Dragonspear add-on installed and installed without the add-on), only pure Rangers can get the animal companion ability. Multiclass Ranger/ Cleric and no Druid class get the ability.
I tested the following cases:
Human Ranger (stalker kit) yes
Human Druid (no kit) no
Human Druid (Totemic Druid) no
Human Fighter (Berserker), dual to Druid no
Human Cleric (Helm), dual to Ranger yes
Elven Ranger (stalker kit) yes
Half-Elf Druid (Totemic Druid) no
Half-Elf multiclass Fighter Druid no
Half-Elf multiclass Ranger Cleric no
Otherwise, the mod works great, although it does throw off the balance of SCS significantly. I took a bear with my Stalker and "Buddy" was super tanky (except against poison).