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:

Show

), 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).