Zyra's build is pretty straightforward. You go pretty much full damage and pop your enemies. She's one of those supports you don't really need to build utility on because it's already so omnipresent in her kit.
Her core items are:

Situational items are:

I'm not particularly sure why that build you posted would recommend building
on Zyra when she's not typically trying to be that close to opponents to have it matter.