I don't know what to call it, it's not steampunk, but you have an ancient chinese setting with modern technology. Magic & social media co-exist. Mythpunk, swordpunk, or elfpunk perhaps.
I'm not as familiar with the original Xiyouji/Saiyuki as I am with Gensoumaden Saiyuki, but I can tell there are some parallels between characters.
Tang is Sanzo/Xuanzang but with Gojyo's penchant for being a self-claimed lady'sman while having intense bromances.
Sun Wu is obviously Sun Wukong/Son Gokuu. The way Sun & Tang met was like 50% Sanzo rescuing Gokuu from his rock prison, & 50% Inaho Hitomebore awakening Alucard Mosquiton with blood, thus creating a magic bond.
Guanyin is Kanzeon Bosatsu, but instead of being a hermaphrodite, he changes sex depending on the time of day.
Ksitigarbha is Guanyin's estranged boyfriend. He was a Bodhisattva who became a demon.
Pleasure Buddha is probably Ni Jian-Yi.
Bai is one of two completely female characters. She's a funny snake demon the audience loves & has slight fujoshi tendencies.
Chang'en was a female fox demon who became a crossdressing male moon god after slaying the god of war. He religiously stalks his ex-boyfriend.
Hou-Yi is the reincarnation of Nataku. He is super mad at Chang'en because of how many times he's caused him to die & reincarnate, but still loves him.
Xian'er is the other completely female character. Readers initially dislike her but warm up to her over a period of time. She is mildly shipteased with both Tang & Bai. She actually seems to be like a female version of Tang, personality-wise.
Hsu / Qing'er is a suspicious guy who hangs around the outskirts & seems to have business with a few of the characters & unknown motives.