This is a problem I encounter with people (and complain about on BB) on a regular basis. Anything and everything one can think of exists because thoughts themselves are real. The human brain constantly symbolizes, but is often not clear on what (and what kind of existence) it is symbolizing. It is a fundamental problem and fairly easy to understand - provided that one is aware that one does not directly perceive the outside world, but only perceive analogies one constructs loosely based upon it.
The classic philosophical rumination asks “Is the thought of a unicorn real?”. Everything is real, but you may or not know what it really is, or represents, or signifies. It is easy to objectively measure that thinking of a unicorn occurs. They popularly symbolize concepts such as love and innocence, which also demonstrably exist. Those who might complain that “that’s cheating” or sophistry because unicorns aren’t demonstrated to exist as actual animals is only demonstrating a lack of understanding of what mythology is and how the mind works.
The video I think is in error by framing this in terms of existent/nonexistent, real/unreal because “thinking about something which doesn’t exist” presupposes that thought itself does not exist, which would be a very troublesome and difficult premise to start from. The reason they frame it this way is for purposes of easy accessibility because so many people misunderstand the actuality behind it. Also, the recursion of thinking about thoughts and symbolizing about symbols is to a large extent what makes human cognition so powerful.