What is the ruling on playing a strategy game for entertainment, knowing that the manufacturing company is Israeli, and that no money is spent on it whatsoever?

The parameters for the permissibility and prohibition of electronic games have been previously explained. The fact that the company producing the game is Israeli does not necessitate its prohibition, nor does it prohibit paying money to acquire it. For dealing with disbelievers in buying and selling is permissible, as the Prophet, peace and blessings be upon him, dealt with the Jews. This is exemplified by his giving Khaybar to the Jews to cultivate, with half of the produce as payment, and his purchasing food from a Jew by pawning.