If a magic item requires attunement but doesn't specify that it needs to be by any classes or a spellcaster, it can be attuned to any one creature. E.G. (requires attunement).
If a magic item has specific prerequisites for attunement, such as a spellcaster or classes, it is stated (in parentheses) and can only be attuned to a creature that meets those specific requirements. E.G. (requires attunement by a spellcaster) or (requires attunement by a bard, cleric, or druid).
If a magic item doesn't require attunement at all, it can be used by anyone.
This is how it's intended to work and it works as intended unless official errata comes out and states otherwise.
To back up these claims we have page 136 of the DMG:
Some magic items require a creature to form a bond with them before their magical properties can be used. This bond is called attunement, and certain items have a prerequisite for it. If the prerequisite is a class, a creature must be a member of that class to attune to the item. ¹
So if we look at the Wand of Magic Missiles, it doesn't require attunement at all so it can be picked up and used by anyone at any time (so long as it still has charges left).
If we look at the Wand of Enemy Detection, it requires attunement but doesn't specify that it needs to be by a spellcaster so it can be attuned and used by any one creature.
And if we look at the Wand of Fireballs, it requires attunement and it's specified that it needs to be by a spellcaster so it can only be attuned and used by a spellcaster. ²
While it doesn't say anything about the requirement for being a spellcaster, the same rules apply (you need to be a spellcaster to attune to the item).
See this question with regards to what is considered a spellcaster for the purposes of attunement.