Hi xchcui,
I don't grasp it neither, as I too expect an "oil" to be a liquid. But it could simply be a matter of wording or of translation, meaning "lubricant" in the original language.
The mix of isoparaffins C10-C13 is indeed a solvent, 1 day is a decent time for their evaporation, and they do lubricate a bit like any paraffin despite being too runny. Comparable to kerosene or Diesel oil, which do lubricate when no thicker oil is possible. I believe this mix comes from the alkylation unit of a petrol refinery, which produces some isoparaffins heavier (C10-C13) than is desired as an anti-knocking additive for high-octane gasoline. These heavier isoparaffins are supposedly removed and sold separately. I had already a solvent bottle of them.
What could make the rest? If your key feels dry, it's not a liquid oil nor a grease (for mechanical engineers, a grease is an oil complemented with a soap, usually a lithium salt of a fatty acid).
My bet, nothing more, is a mix of paraffins that are solid at room temperature. They dissolve in shorter paraffins, they lubricate a bit, and won't evaporate too quickly.
Maybe these paraffins a near the liquid-solid limit. But they could also be much longer. For instance thin polyethylene or polypropylene, possibly as a powder, lubricate metals and aren't dirty like graphite or MoS2.