According to Wikipedia, a kind of hide-and-seek-like games is attested in Ancient Greek as apodidraskinda.
Are there attested similar games in Ancient Rome? If not, are there any good options for the translation?
Just apodidrascinda is valid Renaissance Latin. The k is instead spelled with c as per the classical Romanization of Greek.
Caeterum * apodidrascinda est, hic quidem in medio conniuens considet, aut alius eiusdem cohibet oculos, hi uero occulantur ipso autem ad inquisitione confurgente, quemlibet oportet ipsum in locum suum praeuenire.
This is written in the Latin alphabet, unlike some words written in the Greek alphabet on the next page. This means the translator considered apodidrascinda a valid Latin word.
Julius Pollux wrote the original book Ὀνομαστικόν. Rudolf Gwalther translated Onomasticon in 1541.
For a freer translation, there is this. Although Ἀπόδρασις is a different word, it is a related concept.
8 Ἀπόδρασις στρ. ] Ἀπόδρασις στ. militia detrectatio, fuga. Kühn
You could use that word. Though detrectatio appears to be a rare word, so you might need to use a phrase with lūsus.