Is there rules against posting videos on The Impossible Game?

If you post a short clip with analysis and commentary, it might be Fair Use as a review.

This is very interesting question. Ultimately, there have been many lawsuits against YouTube alleging copyright infringement for the posting of copyright protected material. However, what these cases have shown is that the ultimate liability resides with the individual uploading the copyright protected material. Consequently, your proposed conduct could constitute copyright infringement. Such conduct would normally require a written license. Remember, copyright rights cannot cannot be divested unless in writing signed by the copyright owner.