The 'German Time Game' is confusing (at least to a native). The answers you want to hear are words you would say about a digital clock, it's highly uncommon to use this to tell the time from an analog clock. Maybe you should consider showing a digital clock for this game. What you would use for an analog clock is what you call 'Time Short Form'.
We have been told that it might be normal to tell the time like that from an analog clock in places where precision matters (like train stations or airports). As a beginner, this is how we started to learn it as well in the course I am taking. I think it makes your brain work harder by making it do more processing (you need to interpret the clock + the numbers, whereas a digital clock simply gives the number to you,…
That is true. That is called e.g. 'Bahnhofszeit' and follows different rules than normal time telling. You should include that in the game description, otherwise learners may think that is how you tell the time to each other in everyday life.
I think it is less about precision as e.g. 'zwei vor dreiviertel Elf' is as precise as 'zehn Uhr dreiundvierzig', but more about the way of measuring times. E.g. you do round normal time, but truncate 'train station time'.