I was thinking it was a holdover for holding the tools that go with oil lamps, but you are right, it is for carrying the lamp around, the tools go further down:

Try hanging it from a ceiling hook?

this

How do you know it's not an emergency handle to grab on to in case gravity inverts?

Yeah, I guess it keeps you far enough away from the light/heat source to avoid burns. But in this day and age of LEDs, it's rather vestigial. Maybe you can make a game out of flicking rubber bands through the hoop?

Yeah, from the pics in other posts I'm wondering if this is just a very old lamp. Following the blueprint of its gas predecessor without any thought of what was no longer necessary...

Like a beta of an electric lamp? Before they realized the downsides of a wired connection compared to the "wireless" gas lamp predecessors.

Yup, I wouldn't be surprised to learn that this one was converted from oil to electric.