Frequency Modulated Continuous Wave Radar: Basic Confusion
The receiver's output is not the red line. Instead, it is the beat frequency between red line and blue line. f(beat) = f(blue)-f(red) = fb;
The receiver calculates fb, which is the center frequency shown in FFT diagram. Knowing fb, you can calculate R from the formula $$R=c*Ts*Fb/2Bsweep $$
Check out slide page 9. The diagram you posted indicates the condition when the detected object does not move. What may happen if the object moves? If the detected moves relative to receiver, doplar effect will start to work. Therefore you have a different frequency, which is doplar frequency. 


Check the bottom diagram of slide page 9, it shows the condition when the object move: combination of doplar effect and previous frequency shift.


I guess you may need to know one point. The transmitter is keeping sweeping the frequency, which is indicated by the blue line. In the diagram in page 9, the frequency increases and then decreases and keep doing that in cycles. As a result, beat frequency has the pattern shown. You can get both distance and speed from the beat frequency.