The replacement of silicon might happen 10 years from now, or even later, it is not something that will happen before 2030.
So these transistors are neither for desktop chips nor for mobile chips, but for all of them. Nevertheless besides molybdenum sulfide (this article) and similar materials, there are other 4 or 5 alternatives, e.g. diamond, carbon nanotubes and others. It is not known for sure which will be the winning technology for replacing silicon.
All the alternatives for silicon have currently various problems that must be solved in order to make possible their practical use.
This paper appears to solve one of the difficult existing problems. Molybdenum sulfide and a few other similar materials can form an active single-crystal layer suitable for making transistors in it that has a thickness of only one atom. Therefore using such a material will achieve the smallest possible thickness. A smaller thickness is a precondition for reducing also the horizontal dimensions that determine the transistor density per area.
The problem is that over the semiconductor layer, one has to deposit an insulating layer in order to make a MOS field-effect transistor. While for the semiconductor layer it was known how to make an almost perfect layer only 1-atom thick, depositing over it an insulator resulted in a layer with non-uniform thickness and with many defects.
This paper shows a method that creates an insulating layer with a similar thickness and uniformity as the 1-atom thick semiconductor layer on which it is deposited. This greatly increases the chances that it will become possible to make integrated circuits with such materials instead of silicon.