This is not a grammatical phrase in Latin. It looks like it might be the product of an online translator which produces a word-for-word translation with no regard whatever for Latin syntax.
Ludus
The latin word for game is Ludus, which also means school and sport.
Ludus
Ludus (-i, m).
Training camp for gladiators.
Ludus.
Training camp for gladiators.
The largest gladatorial training school in Rome.
Literally, "household game" though it is sometimes applied to academic institutions and means then a "philosophical school" or "training establishment"
Well, ludus magister would be "school captain". Ludus, ludi, masculine Magister, magistri, neuter
An ancient Roman elementry school was called a ludus.
a play = ludus a theatrical play = fabula to play = ludere I play = ludo