Let's say the bad guy has a Wand of Fireballs, and wants to blast the party with it. To do so, they must:
…use an action to expend 1 or more of its charges to cast the fireball spell …
The party wizard wants to stop this and uses Counterspell which says it:
You attempt to interrupt a creature in the process of casting a spell.
My thought is that this won't work. First, let's remember that when a character casts a spell, they use the Cast a Spell action. There are always components involved, whether verbal, somatic, and/or material.
Using a magic item requires none of these things…it just takes an action. But…what kind of action does it take to use a Wand? Well, according to the Player's Handbook (Combat > Actions in Combat), it would be the Use an Object action (emphasis mine):
You normally interact with an object while doing something else, such as when you draw a sword as part of an attack. When an object requires your action for its use, you take the Use an Object action.1 This action is also useful when you want to interact with more than one object on your turn.
Lastly, the spell description for Counterspell says that in order to cast it, you use your Reaction:
which you take when you see a creature within 60 feet of you casting a spell
So, while the players could certainly see the bad guy with the Wand, they'd see him using the Wand, not casting a spell.
I looked around this Stack, and didn't find this question – which seems a little strange. There is a question (Can you Counterspell a spell-like ability) that deals with spell-like abilities, but not magic items.
To keep the scope of this question narrow, I'm just asking about magic items that state they require an action to use and their use casts a spell.
Can you Counterspell a magic item?
1: The DMG basically has the exact opposite wording regarding the activation of magic items (Ch 7 > Activating an Item) found here. Not sure why these two core rule books directly contradict each other – hopefully that'll be addressed in a Sage Advice someday.
Best Answer
If you're casting a spell, you're casting a spell
The "cast a spell" action isn't the only way to cast a spell. There are a number of other ways to cast a spell. Some spells can be cast as a bonus action or a reaction, and some magic items allow you to cast spells using them, which, as you note, involves an action specific to the item rather than the "cast a spell" action. Regardless of what action, bonus action, or reaction you took, you are still casting a spell, which means that spell can be countered (in theory at least; see below for issues that might arise in practice).
Of course, in the case of magic items, you only cast the spell if the item says so. For example, drinking a potion of growth produces the effect of the enlarge/reduce spell, but it doesn't involve casting that spell, so it cannot be countered. But using a wand of fireballs does involve casting a spell, so it can be countered.
Ask your DM whether magic item use is perceptible
However, there is one other important aspect to counterspell, which is that the caster must see the target casting a spell in order to react to it. Thus, a sorcerer casting a V,S spell with subtle spell metamagic cannot be countered, because the spell has no components to perceive. Interestingly, casting a spell from a magic item also requires no components, so a strict reading of RAW suggests that casting a spell from an item is imperceptible and therefore cannot be countered (unless the item's description mentions a perceptible requirement for use, such as a command word or hand motion).
On the other hand, your DM might find this nonsensical and instead rule that the action required to activate the item and cast the spell is indeed perceptible, allowing the spell's casting to be perceived and countered. So you should talk to your DM and find out how they feel about this before relying on it in play, because whether or not magic item use is perceptible is something your characters should already know, not something they should be finding out in the middle of an important battle.