What is the ruling on playing games from which the unlawful part has been removed and the permissible part played? And is one who plays games produced by a company that has produced games offensive to Islam considered an unbeliever?

If it is possible to remove the Shariah violations from the game, making it free from them, then there appears to be no impediment to playing it. The company's production of games offensive to Islam does not necessitate prohibiting the purchase of their permissible games, and playing them is not an act of disbelief.