Contextual alternates are normally used for certain scripts, like Arabic, where the shape of each glyph depends on the surrounding glyphs. And they are also used for cursive handwriting fonts where the stroke of the “pen” might have different connection points across letters. Texture healing is a novel application of this technology to code.

basically fonts were already capable of using alternate versions of characters based on their nearby characters, so they used that for these fonts to allow for seemingly-dynamic sizing/spacing

Open type fonts have these capabilities built in. It's up to the designer to implement it in useful ways like this.

It’s in the article:

This swapping is powered by an OpenType feature called “contextual alternates,” which is widely supported by both operating systems and browser engines.