The increased density of argon increases the risk of an industrial accident as you note, but I'd expect all inert gases to behave about the same once inhaled. Note that "chemically inert" doesn't always imply "physiologically inert", since e.g. xenon is an anesthetic. Argon is reported to have similar anesthetic properties at elevated pressure, but not at ambient pressure. So I wouldn't expect much difference between argon and nitrogen here.
In any case, that hypoxia routinely causes tragic and avoidable industrial fatalities. Loss of consciousness will occur more quickly than if you just hold your breath, since oxygen not only fails to diffuse in but actually diffuses out. The question of how quickly has apparently received some expert attention, in the context of the death penalty by nitrogen asphyxiation. Two professors write:
Copeland et al. (2015) based their report, in part, on the work of Ernsting (1963) and posited further that 'inhalation of only 1-2 breaths of pure nitrogen will cause a sudden loss of consciousness'. Considering that the one to two breaths were normal tidal volumes of 0.5 L, these would dilute the initial ~16% O2 in the lungs to 14% on the first breath and 12% on the second breath. This might lower arterial PO2 from its normal 95-100 mmHg to ~50 and 36 mmHg, respectively, but would certainly not reduce the arterial O2 to the level that might result in a loss of consciousness. However, both values are consistent with providing an intense respiratory stimulation and dyspnoea via the carotid bodies. Moreover, at a normal breathing frequency of ~15 breaths/min, the 17-20 s elapsed before Ernsting's subjects lost consciousness allows for at least four or five breaths, and far more if the subject is hyperpnoeic and hyperventilating owing to nervousness and the carotid body response to the falling arterial PO2.
https://pmc.ncbi.nlm.nih.gov/articles/PMC11215468/
Those professors were writing in opposition to that method, so they perhaps have some incentive to understate how quickly it causes unconsciousness; but considering the common practice of inhaling helium from balloons, I think they're probably right that it's slower than "1-2 breaths". That said, there are many reports in the literature of people losing consciousness from the balloon trick, so it's not that far from the edge.
In an industrial accident, loss of consciousness is likely to result in death unless rescuers manage to remove the victim (without dying themselves) or ventilate the confined space, since the victim is typically surrounded by thousands of liters of the asphyxiant. That "Lamp of Invisible Light" contraption is about 300 mL, which seems insufficient to directly cause death--a user who loses consciousness but continues breathing will probably exhale the one breath of argon, then inhale normal room air and eventually recover. A balloon may also be relatively safe, while inert gas flowing directly from a cylinder may present extreme danger.
With that addressed, the biggest acute risk here is probably a secondary injury following loss of consciousness in a dangerous situation, like a burn, drowning, or fall. DMT and analogs inherently bring that risk, and have in fact killed people that way vaporized normally, including a friend of a user of this forum; so take due care. As to longer-term risks, that paper notes that strangleholds in judo are held by some competitors to the point of unconsciousness, without obvious harm. A study on prisoners and psychiatric patients used an inflatable cuff with similar effect, also "without apparent gross injury":
By occluding the carotid arteries, inflation of the Kabat-Rossen-Anderson cuff induces acute brain anoxia without affecting breathing or evoking the dyspnoea that attends carotid body stimulation via breathing pure nitrogen. Like shime waza, the acute procedure resulting in loss of consciousness is well tolerated, followed by rapid and uneventful recovery upon release, and can be repeated without apparent gross injury to the subjects (Rossen et al., 1943; Smith et al., 2011).
So that "Lamp" seems relatively safe to me, though I can't immediately find any case in medicine where a mixture that hypoxic is deliberately inhaled. A smaller volume would be safer. The contraption could also be filled only partially for vaporization, then diluted with air before inhaling. The fire hazards of pure oxygen seem like a bad tradeoff for a slightly less hypoxic mixture, especially with a heat source in the vaporizer.
I think the risks of a limited volume of inert gas for vaporization are probably small. I don't think they're zero, especially to the extent either the hypoxia or a physiological effect of the not-quite-inert gas could be synergistic with the intended drug. Any new method may carry new and unknown risks, and I'm glad to see that noted here.