See the article for more details, but abilities such as Zyra'sRampant Growth are not classified as pets and will trigger the slow like any standard abilities.
Rylai is the name of the Crystal Maiden hero in DotA. Rylai specializes in using ice-based crowd control abilities to disable and slow her opponents. The icon for the Crystal Scepter is almost identical to the icon for the Crystal Maiden's and Archmage from Warcraft 3's Brilliance Aura ability.
Slow duration increased to 2 seconds from 1.5 seconds.
It will now trigger on dealing non-periodic spell damage, instead of spell hit. This means that spells like Destiny or Time Warp, which previously triggered the effect, won’t anymore; however, Rupture will now slow on dealing damage instead of on the initial cast, Powerball will now trigger the effect when you hit units, etc.
Slows from items will no longer stack. (i.e. Frozen Mallet, Rylai's Crystal Scepter) The largest slow will take effect until duration wears then next largest slow will take effect if it’s still active.