Görmek is the rootmost word. "To see" Remove infinitive -mek to get to the root of the verb, gör-.
Gör-üş- adds on a mutual-reciprocal ending to the root verb. ("To see each other, meet")
Görüş-ür adds the wide tense/aorist, implying a generally done activity.
Görüşür-üz adds the first person plural. So "We see each other".
So it means "we'll see each other [later]!" Hence is used as a parting.
Try clicking the speaker button to hear a different TTS compare two endings with Z vs S. The Z sound is there.
Turkish does do syllable final devoicing for stops and c/ç in some words, generally of two syllables, and it's reflected in the spelling. E.g. kebap vs. kebabım, vücut vs vücudum, ağaç vs ağacım, and erkek vs erkeğim (where the g undergoes an extra process to make it a glide or vowel lengthener).