I thought the same thing on this until reading multiple posts. However, all infusions require touching a non-magical item, so the argument I keep seeing from the people claiming it is not allowed, is that "simple" just means not "martial" from a classification for proficiency.
The logical statement that the thunder gauntlets and lightning launcher are doing elemental damage and magical effect to the creature hit by the attacks, being magical would mean they are not viable infusion targets. Regardless of the D&D Beyond interface restrictions. Some people would claim that they are inventions of science, and therefore not magical. However, the Thunder Gauntlets even use the phrase "magically" in their description:
Thunder Gauntlets. Each of the armor’s gauntlets counts as a simple melee weapon while you aren’t holding anything in it, and it deals 1d8 thunder damage on a hit. A creature hit by the gauntlet has disadvantage on attack rolls against targets other than you until the start of your next turn, as the armor magically emits a distracting pulse when the creature attacks someone else.
At this point, I would argue that by the verbiage of infusing nonmagical and this description, you cannot enhance weapon thunder gauntlets.
However, the entire argument is thrown upside down when you read the armor modifications ability for level 9
At 9th level, you learn how to use your artificer infusions to specially modify your Arcane Armor. That armor now counts as separate items for the purposes of your Infuse Items feature: armor (the chest piece), boots, helmet, and the armor's special weapon. Each of those items can bear one of your infusions, and the infusions transfer over if you change your armor's model with the Armor Model feature. In addition, the maximum number of items you can infuse at once increases by 2, but those extra items must be part of your Arcane Armor.
This clearly states that the armor becomes 4 parts and each (including the special weapon) can bear one infusion. This makes it contradictory to everything else.
Outcomes on this could be any of the following:
The thunder gauntlets are always magical and can never be infused
Before level 9, when your armor is not considered multiple pieces, you can only imbue the armor with armor specific infusions
Before level 9, you can imbue the armor with either armor infusions OR enhance weapon, but not both because the special weapon is part of the armor you are wearing
At level 9, you gain the ability to infuse your special weapon in a way you couldn't before because of your artificer's skill level
There is no clear final final answer from Jeremy Crawford that I have seen. If someone finds a final answer from Jeremy, please share.