By RAW, no.
The Use Magic Device feature lists the specific attunement requirements that it circumvents, and, as the question states, "spellcaster" isn't one of them. There are other attunement requirements that Use Magic Device doesn't get around — for example, alignment restrictions exist for a Sword of Answering or a Talisman of Pure Good (or Evil).
If the intent was for Use Magic Device to get around all attunement restrictions, then it would say so; we can infer that the intent is that some such restrictions cannot be avoided.
It's possible that the intent of the designers was to allow rogues with Use Magic Device to be able to use the (mostly) wands with the 'spellcaster' restriction, but so far the wording of the rules doesn't support that.
But probably by RAI, yes.
In this Twitter post from October 2016, Jeremy Crawford was asked about how a Wand of Paralysis is used by a rogue, and he doesn't say that it can't be done. But the applicability of Use Magic Device to the spellcaster attunement requirement wasn't the subject of the question, either.
However, this doesn't seem to be a critical game balance issue, and given that Use Magic Device is intended to allow rogues to use spell scrolls, it doesn't seem unreasonable to extend it to the "spellcaster" items as well.
The attunement ends
This can be found in the DMG section for magic items. In the attunement section (DMG p. 138):
A creature’s attunement to an item ends if the creature no longer satisfies the prerequisites for attunement
So if you no longer meet the prerequisites the attunement simply ends
Best Answer
Anyone can attune to the Gauntlets of Ogre Power
You can read up on attunement in the freely available basic rules.
Here are a few of the most relevant excerpts:
So, you can wear them as normal gauntlets fine without attuning - but you you won't get boosted strength until you do attune to them.
So when you ask 'What am I supposed to attune it with?', the answer is that nothing extra is needed - just you, your item and and bit of quality time.
Attunement prevents one character having too many powerful magic items - as any given character cannot attune to more than three at a time.
Some items do have prerequisites - the gauntlets do not.
The gauntlets' rules text states 'Wondrous item, uncommon (requires attunement)'. So they don't require any prerequisite, beyond having a free attunement slot - and even if you don't have an empty slot you can simply un-attune to one of your previously attuned items and free the slot up for the gauntlets.
An item that did have a prerequisite, such as a Pearl of Power, would state that requirement explicitly. For instance, the Pearl's rules text states 'Wondrous item, uncommon (requires attunement by a spellcaster)'.
That said, wearable items do have a sort of hidden prerequisite, unrelated to attunement - they must be worn as intended:
That means that someone without hands could not use the Gauntlets of Ogre Power. You wouldn't gain the benefit, if for instance, you wore them, somewhat clumsily, on a string round your neck. Sadly even a one armed character would be unable to use them - they must always be worn in a pair.