The ATIS lists all available runways, because it use dummy runways to allow crosswind runways to work. Those dummy runways are not used by AI or the ATC, but they will show in the ATIS, it's a known side effect of this method.
This, however, doesn't have anything to do with the ATC Approach selection which, instead, is handed from the Approaches, giving preference to runways with an ILS, and wind direction.
Fact that you are assigned a runway that doesn't have an ILS, seems to indicate another scenery has removed the Approaches. KLAS doesn't come with approaches in its AFCAD, it relies on the one coming from the default scenery so, if another scenery has removed them, or you edited the KLAS AFCAD with an editor that doesn't preserve the approaches, the ATC will rever to taking just the longest available runway.
So, check you are using the AFCAD that comes with KLAS, check it hasn't been modified, and use the free FSX Airport Scanner to find conflicting AFCADs.