[RPG] Does the Armorer Artificer add their Strength Modifier to damage rolls for the Thunder Gauntlets

Your armor's gauntlets don't occupy your hands while worn

While in use, armor is worn, not carried. So the gauntlets that are part of the armor you are wearing don't occupy your hands, even while they "count as simple melee weapons". This means that even though you have a weapon available on each hand, your hands are still free to perform the somatic components of spells or perform any other action. (This versatility is one of the benefits of the Arcane Armor feature.)

You can use your arcane armor as a focus while wearing it

Normally, you need to (be able to) hold the material component of a spell in your hand in order to cast it:

A spellcaster must have a hand free to access a spell's material components -- or to hold a spellcasting focus -- but it can be the same hand that he or she uses to perform somatic components.

So you might be worried that you have to take off your armor and carry it in order to cast spells with it. However, the Arcane Armor feature specifically overrides this general rule, because the ability to use it as a spellcasting focus appears in the list of benefits you gain while wearing the armor, not carrying it:

You gain the following benefits while wearing this armor:

• [...]
• You can use the arcane armor as a spellcasting focus for your artificer spells.
• [...]

In fact, since you gain these benefits only while wearing the armor, this means that you actually cannot use your armor as a spellcasting focus while holding it. Contrast this with infusing a suit of armor with Enhanced Defense, which would technically allow the artificer to use the armor as a focus while holding it rather than wearing it. (Of course, if you infuse a suit of armor with Enhanced Defense and then also use your action to turn it into your arcane armor, then you would be able to use the armor as a spellcasting focus while either holding or wearing it.)

D&D 5e does not distinguish between main and off hand.

Nowhere do the rules make a distinction between main hand and off hand.

The Thunder Gauntlets are not light melee weapons.

Now, for the purposes of two weapon fighting, you cannot use the gauntlets to make a bonus action attack, as two weapon fighting requires each weapon to be a light melee weapon:

When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.

The gauntlets do not have the light property:

Each of the armor’s gauntlets counts as a simple melee weapon while you aren’t holding anything in it.

They both get the bonus.

The “special weapon” of the Guardian Armorer is:

Each of the armor’s gauntlets

Each gauntlet is itself a weapon, and each gets the bonus from your intelligence modifier to attack and damage rolls.

Each model includes a special weapon. When you attack with that weapon, you can add your Intelligence modifier, instead of Strength or Dexterity, to the attack and damage rolls.

I know it says “weapon”, singular, and the guardian technically gets two, one for each hand.