Can a non-player beast benefit from a magic item's effects? For example, would a cat that was wearing a headband of intellect get the extra intelligence the item gives?
All creatures can benefit from and use magic items subject to their anatomical limitations and other capacities.
For example, a creature without a head cannot use a Headband of Intellect and a creature with a head but without the knowledge and understanding of magic items (like most beasts) would not know to wear it. Of course, if someone else were to put it on their dog, say, then it would benefit and now have intelligence enough to work out what's going on.
Volo's Guide to Monsters specifically calls out beholders as wearing rings on their eye stalks and using wands through telekinesis.