I assume it means the user input handler is given a deterministic time slot to do stuff. Regardless of what the operating system is doing, it will always schedule mouse movement (or something along those lines). It's a software implementation (scheduling), but it requires hardware that can support it - usually you need fine-grain control over interrupts. So typically nowadays you see RTOSes on microcontrollers (eg ARM). Maybe more precisely you need access to that fine grain control and that often means getting hold of datasheets that are under strict NDA (eg Broadcom).

RTOSes are often found in autopilot and vehicle management systems controlling critical peripherals or safety critical software. More mundanely there are also sensors that will get upset if you don't give them undivided attention for fixed periods of time (or if you interrupt them, they will terminate the transfer). Image sensors are particularly picky about this.