The code isn't particularly clear (nothing written in Rust is) but it looks like the output is using linear interpolation to compute the values in between steps

The code isn't particularly clear (nothing written in Rust is) but it looks like the output is using linear interpolation to compute the values in between steps. If you use a lookup table then you're approximating a sine as a bunch of piecewise linear segments with surprisingly little error, and linear interpolation works well on those. You don't have any harmonics to worry about and the curve is incredibly smooth, so there are no odd effects to take into account. A while ago I wrote some Python code to demonstrate this effect in calculating frequency from pitch in synthesizers by interpolating a table of semitone steps. The error was negligible up to around C6, which is the top key of most 5-octave keyboards, and only a handful of Hz at C8 which is higher than most folk need. I can't find the code now but when I do I'll post it.