What is the ruling on watching video game clips after intending to postpone them until after Ramadan, and is an expiatory oath (kaffarat yameen) obligatory for that?

No expiation is incumbent upon you, for an oath is not concluded by mere intention, nor by writing without intention according to the majority of scholars. As for video games, their ruling is dependent on their content, as most of them are not free from legitimate religious, psychological, social, or health concerns, including: depicting wars between the people of Earth and the people of Heaven, or glorifying the cross, or extolling magic, or harboring hatred towards Islam and Muslims, or glorifying disbelievers, or containing nudity, or gambling, or music, or causing physical harm, or instilling violence, or corrupting a child's sense of reality.