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.
Training camp for gladiators.
Ludus.
The largest gladatorial training school in Rome.
Well, ludus magister would be "school captain". Ludus, ludi, masculine Magister, magistri, neuter
Literally, "household game" though it is sometimes applied to academic institutions and means then a "philosophical school" or "training establishment"
An ancient Roman elementry school was called a ludus.
a play = ludus a theatrical play = fabula to play = ludere I play = ludo