The game is most likely usually also called "Murder Mystery" or "Murder Party" in Portuguese, like it is in French and Italian and in this Lisbon webpage.
One could say "jogo de mistério" ("mystery game"), but this is rather a class of games. Another possibility could be "[Jogo de] Mistério de Assassinato", but it doesn't really seem to be used.
I suspect that's due to such games not being popular enough in Portuguese-speaking countries.
Another puzzle game, Escape room, is often called by its name in English, even though it does have a Portuguese version of the name, "Jogo de Fuga". Also the game "Clue" (mostly "Cluedo" outside the US) most often keeps its foreign name in Portuguese, even though it could easily be translated (e.g., as "Pista" or "Indício").
Update from OP
I have since by chance found another example of a "murder mystery":
MURDER MYSTERY
O QUE É?
Uma refeição verdadeiramente inquietante é a descrição ideal para o
“Murder Mystery”, um programa totalmente inovador num detalhe
determinante: são os clientes que dão vida aos personagens e resolvem
o crime!
...
O INTERROGATÓRIO
Durante as interações e os interrogatórios os participantes estarão a
ser avaliados pelo staff presente, tendo em conta o cumprimento dos
objetivos atribuídos a cada um inicialmente (3 objetivos secundários e
1 objetivo principal).
As missões são simples e implicam a interação com os outros
participantes. A título de exemplo: “coloque este papel no bolso do
personagem X e exponha-o publicamente quando estiver a ser
interrogado” ou “deixe uma marca de batom na camisa do Padrinho”.
The source is here but note that this is not a recommendation, I have not tried them, and have no affiliation.
