We don't have synonyms for intertainment yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are entertainment and intertwinement.
(n) :
(archaic) Alternative form of entertainment. [An activity designed to give pleasure, enjoyment, diversion, amusement, or relaxation to an audience, no matter whether the audience participates passively as in watching opera or a movie, or actively as in games.]
(n) :
(archaic) Alternative form of entertainment. [An activity designed to give pleasure, enjoyment, diversion, amusement, or relaxation to an audience, no matter whether the audience participates passively as in watching opera or a movie, or actively as in games.]