The notion that the Chinese spent 600 years using gunpowder exclusively for amusement and that it was only when Europeans invented guns in the early 14th century that gunpowder began achieving its full potential is outdated, racist, and worst of all, factually wrong.

As with many things, we tend to look for patterns of familiarity in contexts deemed 'exotic', and for a long time our failure to recognise the use of gunpowder in military capacities in China has been down in part to retroactive assumptions based on the sheer disparity in weaponry seen in the period of the Opium Wars, and in part to the lack of references to recognisable gunpowder weapons, namely the gun (whether as a hand or a siege weapon), before the 14th century. The Chinese indeed are not definitively known to have had guns before the late 13th century. But that is not mutually exclusive with military gunpowder use in general.

Looking at things etymologically, our English term gunpowder implies the substance's use as a propellant in, well, guns, as do the French terms poudre á canon ('cannon powder') and German Schießpulver ('shooting powder'). That the Chinese term is 火藥 huoyao ('fire medicine') hints at its original use – as an incendiary. Gunpowder was principally used in disposable, single-use weapons, as an incendiary, a slow-burning propellant, or as an explosive. The fire-lance, basically a tube of gunpowder (originally made of bamboo and latterly of metal) suspended on the end of a spear, is an example of the first type, as it was intended to spew flames forward of the spear for a period of time, and was intended to be used especially against enemy siege equipment, which, being made of wood, might be lit on fire or at least severely damaged by the flames from the lance. Gunpowder was also used in rockets, though typically as extra propulsion for arrows and other sharp implements, rather than fused explosive charges like Congreve rockets or the Indian designs they were based on. And of course there were bombs, such as in the form of clay hand grenades, or larger examples intended to be hurled by trebuchets.

So why not guns? Firstly, I would argue that guns only seem intuitive if you already know how to make one. If your gunpowder arsenal is primarily used in self-contained, single-use devices, for explosive or incendiary properties, and in weapons that generally don't stay close to their users' hands for very long, then developing reusable hand-held weapons that exploit gunpowder as a propellant doesn't necessarily come naturally. The most reasonable theory for how the gun came into being is that it was a gradual evolution from the fire-lance, which in later incarnations would exploit the propulsive capacity of gunpowder by adding in fragments of stone, metal or even porcelain, which would be launched out along with the flames when the charge was ignited. Transitioning to metal tubes allowed the fire-lance to be reloaded and reused, and going from a progressive slow-burning charge to a single propelling charge was the final step.

The development of the gun thus took quite a long time, as aside from recognising the physics behind gun design, you also needed improvements in not only metallurgy but also, critically, gunpowder formulation (to decrease burning time and increase gas output). Aside from that, one possible reason why guns didn't really come into being in China is that Chinese city walls were very much resistant to bombardment, being largely thick earthworks instead of masonry. It was thus far more useful to hurl incendiaries into a city than waste gunpowder and manpower hurling projectiles into an earthen wall in the hopes of collapsing it.

This is partly why saying that even primitive guns would have been a world-conquering invention is problematic. 'Primitive guns' were relatively small-calibre hand-guns, and broadly anti-personnel rather than siege weapons (our earliest illustrations of European guns, for instance, are relatively small-calibre, and many show them firing bolts or arrows rather than round projectiles). This made them relatively unhelpful against fortifications. Moreover, the basic gun spread across Eurasia very quickly. The earliest known Chinese gun is a hand-gun dated to 1298, discovered at the Mongol palace complex of Xanadu; the earliest depiction of a gun in Europe is a small cannon in an illustration as part of Walter de Milemete's treatise on kingship, presented to King Edward III of England in 1326. While it is logical to presume that gun production in Asia may have started earlier (and there is some archaeological evidence to suggest that the earliest cannons could have been produced as early as 1200), it is not an advantage that East Asia possessed for very long.

Now, you suggested that even primitive guns would have allowed China to conquer the world. Setting aside the logistical, political and cultural barriers, I would note that it is plausible to suggest that that kind of sort of did in fact happen. Because the Mongols invaded China, found out how to make gunpowder themselves (or get their subjects to do it for them), and it has been argued that they were the principal transmission vector for gunpowder technology across the Eurasian continent. Writers in areas of the Muslim world directly threatened by the Mongols, such as Syria and Egypt, were describing gunpowder by the mid/late 13th century, long before Western Europe (which lay beyond Mongol dominion) did. At the same time, there is little evidence to definitively confirm that the Mongols did employ gunpowder weaponry in sieges in the Middle East: both Chinese and Persian sources are ambiguous as to whether Mongol armies in the Middle East used gunpowder proper, or simply saltpetre-based incendiaries, or even naphtha (pitch), the lattermost of which was relatively familiar in the region. So the Mongols did conquer a large part of the world, and they did use gunpowder, but it's not clear that the former followed on naturally from the latter.