I think the argument about pneumatic tyres is irrelevant, and also uninteresting. You could have gear with metal tyres (like a train has). More interesting is why no wheels at all?
Let's look at the role of the gear during take-off. When a Viper is accelerated along the launch tube (presumably using some kind of magnetic rail system, in addition to the Viper's engines) it apparently reaches combat speed on exit. Today's ship-launched jet fighters have wheels and reach take-off speed (in atmosphere), but nothing close to combat speed.
What would be the risk of a wheel fouling in the launch tube, at combat speed? It would probably be catastrophic to the Viper and serious for the Battlestar.
For that matter skids wouldn't be much better, if there was some foreign object in the tube.
Looking at some images on the Net, it seems that for the launch the Viper is mounted onto a catapult under the main fuselage
Those images are both of the same model by model maker Ian Lawrance - awesome work!
My in-universe conjecture here is that the gear are not involved in take-off, only in landing, and the use of skids makes it easier to engineer a gear which can retract to become flush to the fuselage. Also, the Viper's deck operations take place in zero or controlled gravity where wheels would not assist, so they are not necessary.
For real-world thoughts, here's a studio archive image of a Viper prop:
In the real world, it gets better: the '70s studio mock-up skids had wheels
Clearly these wheels assisted in moving the mock-up around the studio, where there's no controlled gravity. But the designer went for skids, presumably for aesthetic reasons. Maybe they felt wheels look too pedestrian.
The Galactica TV page about Viper Mockup also explains that in the real world, the merchandice for the Viper were released before the first broadcast of the show, and these models were designed to re-use parts from other contemporary TV and movie space ships - notably the Star Wars franchise. So the skids likely came from a toy X-Wing or other Rebel Alliance space ship.
The best image I can find of a period Viper toy showing the gear is this pinterest pin which actually has a wheel:
So I'm not sure now, maybe there were other toys with skids. The skids even on the 70s studio mockup and models only look vaguely like an X-Wing skid too.
I recently saw a video of the X-15 space-plane landing at Edwards AFB. It used skids on the rear fuselage, and a wheel in the nose.
A distinct feature of the X-15s were the main retractable landing gears, which used skids instead of wheels for simplicity and weight reduction. The skids, coupled with a non-steerable nose-landing wheel, required the aircraft to land on a dry lakebed rather than a conventional concrete runway
-- X-15 fact sheet, NASA Dryden Flight Research Center
It struck me that this could have been an inspiration for the TV show's model designers, especially since it was a space-plane, like the Viper.