The PCB industry, and PCB layout tools, evolved and matured in places where the so-called "imperial measurement system" predominated. (Where I live, we usually shift the blame by calling it the "English system".) The term "mils", meaning 1/1000 inch, is deeply embedded in our minds, documentation, and software. Some of us gray-haired old men (GHOM) occasionally still use the term "thou", for "one-thousandth of an inch". The industry is moving at nearly a glacial velocity toward using millimeters as the default unit for all distances, but even where this has been proclaimed as the "official" standard the working folks still hang onto inches, mils, and thou.
So yes, when Seeed Studio says "mils", they mean 1/1000 inch.
@Rene_Poschl gave you the pragmatic answer to setting the KiCAD global design rules: Set Preferences to "Inches" (there's a handy button for this on the left-hand toolbar), enter the values for your global design rules, close "Design Rules" and switch back to millimeters. KiCAD's internal calculations are done in nanometers(!) as I recall so the length conversions are carried out to about a dozen decimal places beyond what is significant.
At this time I estimate that the plurality of PCB fabricators provide boards meeting "6/6" rules (6 mil minimum trace width and 6 mil minimum copper-to-copper spacing) as their standard product. However, it may not be wise to design your board right at the edge of their capabilities. (That's a GHOM speaking.) At the very least you should allow for the folks in purchasing who will locate a lower-cost provider who can't consistently produce boards at the limits of your preferred supplier's capability. I routinely set my global rules to 10/10 (mils), and deal with situations where that is not practical on a case-by-case basis. If your board will be manually assembled, hand soldered, or possibly subject to component removal and replacement due to experiments in the development effort, wider traces and more spacing is beneficial.