People are all over the map on this, but here's my thoughts FWIW;
The KLR isn't an ADV bike, especially the Gen1......it isn't technically a dual sport IMO either though it's often referred to as such (even by me). Kawasaki advertised the Gen1 KLR as a "Dual Purpose" bike and I'd suggest that is the most accurate description.
- Dual Sport: KTM500EXC, Beta 500RS, Husqvarna FE501, and similar bikes.....basically dirt bikes that are street legal
- Dual Purpose Bikes: KLR650, DR650, XR650L, KTM690........you could argue the DRZ400 and WRR in either of the first two catagories
- ADV bikes: All the twins; F800Gs, Triumph 800XC, 1200GS, KTM 950/990/1090/1190, Honda AT, V strom, etc. .......big variation in capabilities in this catagory, i.e. AT vs. V strom