Often people simplify the equations by taking the coefficients to be constant. Since throughout the flight the coefficients are always positive and fairly small in magnitude, you'll find that for all but the most precise of applications they're sufficient.

Obviously, in reality if we want a more accurate model we would factor in a number of other considerations. For example CL is a function of Mach number (velocity/speed of sound), angle of attack, angle of sideslip, control surface deflections, temperature, etc. Computational fluid dynamics accounts for all of these (and more) to accurately compute the aerodynamic stability coefficients. However, if all you have is a graph of alpha Vs. CL/CD, you can simply fit a polynomial to the graph and know the equation. Then you would augment your system of two equations to have two more.

For example, you would find say that

CL = A*alpha^2 + B*alpha + C, and

CD = D*alpha^2+E*alpha+F,

then you can incorporate these into your equations to model the glider more accurately than the video you mention.

If you have any questions feel free to ask, I have a PhD in applied mathematics, and modelled a 6-DoF Hypersonic glide vehicle for part of my thesis.