Ludus
The generally accepted word for 'sport' was the same as for 'game' and 'school'. It is 'ludus'. It is a second declension noun.
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.
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.
Well, ludus magister would be "school captain". Ludus, ludi, masculine Magister, magistri, neuter
funis - n. Rope, cord, or line.