I think maybe a better thing to do is to include a new label for the cover of the game box and digital storefronts stating something like “This game contains simulated or real gambling,” rather than an instant R18+ rating. Mario Party being R18+ for example is a bit excessive, IMO.
A trespasser is trespassed from a property by law enforcement at the request of the property owner. This is called a criminal trespass.
Illegally trespassing would be an informal term, and legally or criminal trespassing would the the legal term to describe the act of staying on private property after they have been warned/asked to leave. If you are trespassing in a legal or allowed way, then it is not trespassing.
In most places, a property owner must ask law enforcement to trespass the person off of the property before someone is considered legally or criminally trespassing. In most places a warning, either verbal or by sign or other means, must be given before a person can be criminally trespassed, but that is not automatic as the property owner may choose to not enforce it.