Huge Difference In Density
The farther away you are from the center of mass the lower the gravity if mass were constant. Mass generally goes up proportional to r^2 with additional minor increases due to compression. Jupiter is far less dense than Earth so it has a much more gradual gravitational gradient. Large rocky planets should increase faster in surface gravity with a proportional change in radius than similar ratios between gas giants, but Phil probably did flub the math given he left out definitions and the literature contradiction. Then again we know how unreliable the press is.
The equation is a basic one in any college phycsics text, but I don't have mine handy. I bet phil got the equation right, but misinterpreted one of the symbols.
Regards,
Mark