ANY application can use embedded Linux, not just the ones you mentioned. It is popular because it is free and open source, that means you can modify it for your specific needs.
Understand that Linux is an operating system, the platform for launching other programs so it makes an excellent foundation to run applications you write without you having to write all the input and output routines, filing system support and interfaces. It also very modular so you only need to install the kernel and support for the hardware you need, leaving as much space as possible for other uses. It can also run for the most part in fixed memory which makes it ideal to embed in silicon.
Embedded Linux is available for several processor cores, ARM is just popular because it is fast and economical to use but there are very acceptable alternatives.
Brian.