Yeah, it's strange people are thinking the display of a spectrum analyzer is somehow 1:1 with the underlying thing which they are measuring. As if a digital clock with only the hour and minutes displayed implies that seconds don't exist.

No, you put a low pass filter on the other side of the DAC and it looks equally smooth. Those stair steps are high frequency. This is the filter is called the image rejection or reconstruction filter. Once you learn about the frequency domain, you realize how silly most digital versus analog debates are and how very few really understand what is going on.