The Thing was a listening device used by the Soviet Union to eavesdrop on US government officials. It was basically an AM transmitter if I understand correctly, but it required another transmitter on the same frequency for power. Would it be legal to use a similar device on ham bands (specifically 70cm)? (Obviously, its original use would be illegal regardless of what radio technology is used; I'm just curious if using the technology for otherwise-legal purposes would be okay.)
This device (and devices made later that were improvements on the device), while clever in how it works, could be considered an experimental mode with an interesting modulation scheme.
I don't think there is anything in the US regulations forbidding building and operating such a device as long as this is done in accordance to one's licensing, and in accordance with the regulations related to power, interference, frequency, and bandwidth. National and local bandplans may also have to be checked, at least as a consideration to other amateurs.
But that's more or less true for any radio devices amateurs can think of.
In fact, similar devices might be an interesting variation on the devices and techniques used for "fox-hunting". Admittedly, this might be more of an indoor version of fox-hunting. Still, one could imagine versions of this being used as a way to introduce signal generators, directional antennas, and VNAs into an amateur conversation.
(I suppose it bears mentioning that this design, at least as originally created, deliberately issues RF on harmonics of its designed fundamental. Experimenters would require both the knowledge and licensing to design and build it with care, including any necessary filters to reduce out-of-band transmissions. Or at least know that the device is so low-powered as to not cause such problems.)