The Gadgeteer

[Arkhios]

Arcane Firearm
5th-level Artillerist feature

You know how to turn a wand, staff, or rod into an arcane firearm, a conduit for your destructive spells. When you finish a long rest, you can use woodcarver’s tools to carve special sigils into a wand, staff, or rod and thereby turn it into your arcane firearm. The sigils disappear from the object if you later carve them on a different item. The sigils otherwise last indefinitely.

You can use your arcane firearm as a spellcasting focus for your artificer spells. When you cast an artificer spell through the firearm, roll a d8, and you gain a bonus to one of the spell’s damage rolls equal to the number rolled.

Emphasis mine.

Just what text have I ignored?

Please don't insult. It is a violation of forum rules.

You're ignoring (apparently) the explicit explanation of what the [arcane firearm] is, especially in the subclass feature context, and otherwise. It's explained right after the text telling that you can turn a wand, staff, or rod into an [arcane firearm], and that the [arcane firearm] is a conduit for your destructive spells. In other words, a spellcasting focus (as explained further ahead both above and below).
[square brackets to emphasize that the 'arcane firearm' is one term, not just one or the other]

As JNAProductions said, just because the feature names and (repeatedly) refers to it as firearm, it doesn't mean it's a gun. You can't fire shots of any kind without casting a spell while using it as a conduit for your artificer spells (all of which, by the way, you can't cast without a spellcasting focus, see below).

Remember that all Artificers must use their tools to cast their spells (it's literally spelled out in the class description; it's not an optional feature). Artificers can't "just cast spells" like other spellcasters do. This feature is an extension of it. See below the quote from under 1st-level artificer feature "Spellcasting".

Tools Required
You produce your artificer spell effects through your tools. You must have a spellcasting focus --snip--

Emphasis mine.

Also, stoutstien offers good insight on the matter (I believe this is the Blog stoutstien is speaking of). Anyway, in Eberron, in general staves and wands often double as "sort of magical guns", because in the world of Eberron there are no actual guns given the direction the world's technological advancement has taken; instead of guns the Spellcasting Foci are wielded as if they were guns (but they're not; think of a child using their imagination and pretending that fallen branches or sticks are guns, it's like that).

I can't find the exact text describing this at the moment, but I'm certain I've read it a couple of times from a 5e Eberron related document, book, or booklet. (I thought it was in Eberron: Rising from the Last War, but it might've been in the Embers of the Last War, or the pdf that predated E:RftLW, and I seem to have misplaced my copies of those).

Ah, yes! I found it. Wayfinder's Guide to Eberron specifically mentions that arcane focuses are basically equal to weapons in Eberron, which is a home to Wandslingers. A Wandslinger is not a class, but rather a term describing people capable of casting at least some arcane spells, who use arcane focuses essentially as if they were their weapons, through which they cast their cantrips and other spells.

Go to the Bazaar in Sharn or any enclave of House Cannith and you’ll find a wide selection of arcane focuses to choose from. For a wandslinger, the choice of an arcane focus carries the same weight as a duelist deciding between a rapier or a maul. Do you use a wand of Fernian ash to focus your fire bolt, or do you harness defensive energies with a Risian orb?
An arcane focus is a tool, and only provides its benefits while you’re actively using it. An orb of shielding provides no protection when it’s in your pack; you must have it in your hand.
In Khorvaire, arcane focus items are recognized as weapons: if guards are securing swords and bows, they’ll also require you to turn over your staff.

Also, tangentially relevant:

In Eberron, an arcane focus is a weapon. As such, it can be interesting to give a focus some of the same trade-offs as mundane weapons: do you sacrifice your free hand for greater power?
If you use this optional rule, when a caster uses a two-handed arcane focus to cast an offensive cantrip (a cantrip requiring a saving throw or an attack roll), the range of the cantrip is increased by 50 percent.
By this rule, a staff always requires two hands, while rods can be used with either one or two hands. Using a two-handed arcane focus fulfills the somatic component requirement for a spell.

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AAANYWAY, with all that said, I can understand why a player or DM would want to houserule how the feature works in their game, and that's fine. Even I would probably do that as a DM, if requested, but I wouldn't assume or insist it's the RAW or even RAI.

If or when should I do so, I would probably say that in addition to its normal features, the Arcane Firearm is also a firearm that you have proficiency with. It has a normal range of 100 feet and a long range of 400 feet. The damage it deals is 1d8 force damage per hit, and you use your Dexterity or Intelligence modifier for attack and damage rolls with it. It doesn't require ammunition as long as you wield it. I counts as an Infusion when wielded by you, but doesn't count against the number of items you can infuse. [DM Note]to prevent it from stacking with other infusions[/DM Note]