Fourier transform for non-sinusoidal signal
The Fourier Transform will decompose your non-sinusoidal signal into harmonics, dominantly odd harmonics since your distortion appears symmetrical, and the amplitude as you derive would be the amplitude of the relevant sinusoidal harmonic (so in your case it looks like the fundamental is shown, so we are seeing the amplitude of the first fundamental harmonic which is a sinusoidal signal). It will be less than the peak amplitude shown in the time domain plot, which is the composite of all the harmonics.

Other factors that will effect the amplitude is spectral leakage due to your use of a rectangular window (so to the extent the harmonics fall into a sidelobe of the kernel for your rectangular window) and scalloping loss (to the extent the fundamental frequency is between an integer sub-multiple of your sampling frequency. Both of these effects are described in more detail in my favorite paper by fred harris: fred harris On the Use of Windowing

I am surprised that we do not see any evidence of these harmonics in your frequency plot but this may be because you are only showing a portion of all the frequencies or perhaps because the magnitude is not on a log scale we are not able to make out the harmonics. For example, there should definitely be a signal at three times the fundamental shown. The fundamental appears to be close to 0.04; meaning we should see a harmonic at 0.12; if your frequency of 0.1 represents the Nyquist boundary, then the image of this would be at 0.08 assuming a real signal as you have plotted. (Could you please udpdate your plot to have a log (dB) magnitude scale so we can be sure nothing else is astray?).

That said, we do see that your amplitudes are actually quite close visually from the plot (approx 0.17 in the FFT vs approx 0.19 in the time domain plot), so you must be concerned with the small difference, which is accounted for from the effects described above (the 0.17 is the amplitude of the primary tone as modified by the spectral leakage of your rectangular window and any scalloping loss).