In the case of China, a key point to mention is that 主, variously pronounced as zhǔ (Mandarin), zyu (Cantonese), chú (Hakka), and chí (Hokkien), is one of many titles to refer to the Abrahamic God in particular. It is in fact a contraction of 天主 (tiānzhǔ; tin zyu; thiên-chú; thian-chí), which literally translates to 'Heavenly Master', and is particularly associated with Catholicism (天主教). Protestants tend to prefer 上帝 (shàngdì; soeng dai; song-ti; siāng-tè), which is literally 'High Sovereign', or alternatively 神 (shén; san; sṳ̀n; sîn), a repurposing of a term that had more generally meant 'spirit' in a pre-Christian context. The use of 主 in Chinese languages to refer to a deity is therefore only in a Christian context. Moreover, 主 in Old Chinese is reconstructed as /*toʔ/ and in Middle Chinese as /tsyu/, which further distances itself from Zeus as we pronounce it today, and on top of that Ζηυς would in fact have been pronounced either dzeus or zdeus (whether zetas were pronounced [dz] or [zd] is still debated), moving the two even further apart.

You've already answered the question by asking it. Notice you've referred to "Proto Indo European"? That's the answer to the commonality on most of the deities you've linked (I don't know about the Chinese one)

Basically it goes like this. Many of the languages spread across Eurasia derive from a common root. This family of languages is called Indo European and the proposed hypothetical root language is called Proto Indo European.

The origins of this lie in the arena of Comparative Linguistics, originally called Philology. Basically it went like this. During their time in India, a group of academic colonial officials began to familiarise themselves with Indian culture and language as part of their duties. One of the them, by the name of William Jones, noted the deep similarities in many words between Sanskrit and Greek and over time this evolved into the modern study of these interrelated languages.

One of the things that were noted is that many deities appear common to these cultures, which eventually prompted an exploration into the root community which must have worshipped these deities. It was soon recognised that this root community of Indo Europeans branched out into many directions leading to the various ancient cultures ranging from the Germans to the Romans to the Greeks to the Scythians to Iran and to India. There are many cultures I've skipped over here.

These common deities are all generally believed to represent archetypes and common divinities. Thus you see Sky Father. There is also a Heavenly Oceanic/Universal sky deity which in Greek culture was called Ouranous and in India became Varuna. Similarly the Iranians and Indians had common deities such as Indra and Mitra, though in some cases over time an inversion took place, with the devas becoming gods in India and Demons in Iran, and the opposite happening with the Asuras.

There are today many debates on the "original homeland" of this ancient community of Indo Europeans (oftentimes called the Aryans, though it's a problematic term in its own right)

If you're interested in reading further about this area a good starting point would be The Horse, the Wheel, and Language by David Anthony.