Yeah that sounds roughly equivalent to what I do

Where I am, PD, FD, and EMS are all dispatched out of the same center, and we do start generally with call taking and then eventually get trained on police dispatch, and eventually fire and EMS.

Since the job posting only mentions call taking and police dispatch though, I suspect your area works things kind of like the big city that neighbors my county does

There, 911 calls first go into the police dispatch center, and if fire or EMS are needed the caller is then transferred to the fire department so they can be dispatched and medical pre-arrival instructions can be given.

So in case you're more interested in fire and EMS dispatch than police you may want to look into more specifics of how your area handles that, there might be a similar job posting with the fire department or something you could apply to.

I've actually personally chosen to remain as a call taker only despite being asked pretty much every year if I want to get trained on dispatch.

I have a few reasons for that- one is I just don't particularly want to deal with cops directly that much, I also just think call-taking is the more interesting and fulfilling part of the job, and also it leaves me with something else to move onto if I ever start feeling burned out without having to completely change jobs.

Although I think some of our newer hires who have gone on to dispatch class don't always understand that and think I'm a fuck-up who's getting passed over for promotions. C'est la Vie.