The "growing planet" hypothesis has two major, fundamental problems with it - one regarding its explanatory power, and the other more serious one regarding basic planetary physics
Firstly Everything in the video is fully explainable using non-growing plate tectonic theories. Why are old fish fossils on land? Because plate tectonics moved the plates around, changing sea levels mean some areas that were underwater now aren't. Why are the sea beds geologically so young? Because the plate movements keep recycling. Why does Mars not show signs of subduction? Because it's plates stopped moving around 3.5 billion years ago.
In fact, since most of the Martian surface is about 3-3.5 billion years old this presents real problems for the "growing planet" hypothesis (though not as major as item 2!) Did Mars stop growing? Why? According to standard geology the planet radiated away the heat required to drive its tectonic activity. The growing planet hypothesis has - as far as I can tell - nothing.
Secondly he fundamental physics behind the problem don't add up. Let's do some simple maths.
The growing earth hypothesis suggests that as recently as 60-100 million years ago, the planet was entirely land and has expanded to create the oceans.
The surface area of the planet is approximately 1 part in 3 land. This means that 100 million years ago the surface area of the planet was one third the area it is now. This means the radius of the planet was smaller by a factor of sqrt(3) (~1.7 times smaller). The volume of the earth would have been 5.2 times smaller (3^(3/2)).
The proponent of this hypothesis insists that the DENSITY stayed the same during this period - the mass of the Earth would have been 5.2 times smaller 100 million years ago! Given the mass of the Earth this comes out as a rate of change of mass averaging 1.5 billion kg/s! That's approximately one 50m asteroid strike per second (we're talking Tunguska event sized impacts here...)
If the mass stays the same we're left with very uncomfortable problems from pressure. Isobaric compression to that volume would leave the mantle at the surface at around 4000 degrees Celsius (7300 degrees Fahrenheit). Enough to melt the crust.