If people stopped using Linux on their desktop, will this then be the end of Linux on the desktop?
People use Linux on their desktop or laptop (their workstation), for its the the best option they have to meet their needs. So, for them to stop using it, something else needs to first come along and meet their needs as well as or better than Linux.
The server market has always been Linux strength, and it's been the primary use, and much time & effort & money was invested in Linux to make it suitable for enterprise server farms Since early 2000's for competing against Windows server and other UNIX servers.
Since Linux itself is "free" in most every way - free to alter, free to use, free to give to someone else, free to use in another project, free to compile, free to compile software for - many companies have been researching & developing (R&D) what they can do with it.
Android is essentially a re-branded Linux and makes up most of the telephone and/or tablet market. Ditto with Chome OS for netbooks.
Ubuntu is a company heavily invested in using their own branded Linux everywhere that people are willing to use it.
Many other companies are using Linux for specialty areas (switches/routers) where Linux is suitable.