Does this also apply to more fantasy oriented war games?

No, the ICRC is talking about video games that simulate real-war situations. It is not suggesting that this apply to games that portray more fictional scenarios such as medieval fantasy or futuristic wars in outer space.

A few media reported that certain virtual acts performed by characters in video games could amount to serious violations of the law of armed conflict. Is this correct?

No. Serious violations of the laws of war can only be committed in real-life. A person cannot commit a war crime simply by playing a video game.

https://www.icrc.org/en/doc/resources/documents/film/2013/09-28-ihl-video-games.htm