Is a person considered an infidel if they laughed while watching a video clip of an infidel mocking the Prophet (peace be upon him), without initially realizing the mockery, and then later regretted it and doubted their Islam?

The laughter you mentioned does not go beyond the realm of 'waswasah' (whispers/Mischief of Satan), which should be ignored. According to what you stated in your question, your laughter was not out of mockery, and therefore, you remain Muslim. We advise you to avoid scenes that could be harmful to their viewers.