Okay this blog is wrong. The freq domain representation of an impulse is not sinusoidal. The spectrum of an impulse is spread continuously over a broad frequency range. Maybe the author was playing with an FFT library that they just didn't understand properly.
You're talking about the magnitude, which is spread evenly across the frequency range. The real component of the freq domain representation is in fact sinusoidal. Time-Frequency duality is a well-known phenomenon in signal processing.
> Maybe the author was playing with an FFT library that they just didn't understand properly.