Are "arm pistols" one of those "ackshully it's a brace, not a stock" loophole things?

Not in this case - the idea was to be a very compact PDW, originally for shot-down pilots, who don't have a lot of space in the cockpit to fit in a full rifle, and have historically relied on pistols or janky survival rifles. It didn't pan out (although eventually the USAF would adopt a rifle, but a special AR-15 that can be broken down easily rather than a bullpup:

), and so attempts were made to sell it on the civilian market, but it doesn't seem to have been very popular, since it's ergonomically pretty bad (there isn't even a proper stock to shoulder or any space for your supporting hand to grip it, you're actually supposed to shoot it one-handed as a pistol, which in a rifle cartridge is a dubious proposition).