What is the evidence for the impermissibility of men looking at photographic images, and how can it be said that playing video games does not constitute an acceptance of photography, despite paying money for them and enjoying them?

There is no evidence for the prohibition of looking at photographic images of men. As for the hadiths stating that the Prophet (peace be upon him) would not enter a house that contained images, the response is that this was to reprimand the image-maker and its owner, not to prohibit looking at them. Images that appear on screens, such as television, phones, and PlayStation, do not fall under the ruling of prohibited fixed images because they are not visible to the naked eye and do not come under the prohibition of angels entering a house with images. One who buys these devices does not buy them for the sake of the images within them, but for the purpose of playing, and thus the ruling of prohibiting imaging does not apply to him.