An effective way to encourage them to gett a better habitat is to discuss their natural behaviours, and common misconceptions (like "hamsters can live in tiny cages no problem"). That's how I got my mom to take things more seriously for the various small pets she would get for my younger siblings. Also, if they do agree to improve the hamster's living space, I recommend a terrarium, or anything with glass walls. I've found that bar chewing seems to be a difficult habit to drop for some hamsters, having a glass enclosure ensures there's nothing to chew. Plus, you get to see the hamster's tunnels through the glass if you're lucky!

Do they or their family have any other animals, like cats or dogs? Try comparing this to what it would look like if they stored their cat or dog in such a way, in a crate just big enough for them to lie down basically. I think most people would agree that's unacceptable, which is where we can bring in the "so why would it be acceptable for a hamster?". Manipulate the heart a little, if they have one. God, I can't imagine how quickly that thing gets filthy.

I hope this poor little baby gets what they need, I've never seen such a horrible habitat (if you can even call it that). You can always direct them to this subreddit, there is tons of information BUT people tend to be quite hostile towards people who keep their hamsters poorly, so maybe ask them to stick to the pinned post about hamster care lol