Yes, the media is the gravel, as long as there is surface area, water flow, and the media is fish safe you have a bio filter. Increase the flow you get better mechanical filtration as well.
Just to let you know, I am a DIY freak, if I can make it better or cheaper I will. I will not hesitate to modify nearly anything to improve performance, this includes things like furnaces, dryers, and other household items. Building & modifying filters is a piece of cake. Some day I will figure out how to make aquarium heaters cheaper.
OK, this is the finished product, been making & using these for years.
Here's a pic with the sponge slid up, you can see the holes drilled for water flow, pop can tossed in for an idea of size;
I get the sponge larger from a local shop and cut it down;
There is some gravel in the bottom of the pvc tube, sponge tends to float. You want to use open cell sponge, this allows water to flow through, unlike something like a car wash sponge, which is closed cell. The car wash sponge holds water nicely, open cell sponge will let it flow right out. In this application you want water flow. Cheap cushion foam is usually open cell as well, it's a common WalMart item.
You can make these as large or small as you want, mine are made with 1/2" pvc. You could easily go with a smaller sponge & tubing if needed, or larger if you felt like it. I make these for about half the cheapest price I can find them for online.