Yes that looks like the games list is blocked. Quest connects to
www.textadventures.co.uk to fetch the games list and download games, so you need to ensure that domain is unblocked.
Any games you download are stored locally in your user profile "Documents\Quest Games" folder. You could also download manually from the website using your browser, and then open them from the File menu.
For schools, I'm thinking of having the ability to set up separate "areas", so you could only allow students to download games from your own mini version of the site. This could be customised with just the games you want to permit. Students could submit games to their own school mini-site as well. Maybe that's overkill for your purposes?
Another way would be to have a particular registry setting to filter the list. Would that be something easy to deploy over the school network?