The source for this illustration, the 1814 edition of Alexander's The Costume of China, includes captions for the various plates, so I may as well reproduce that caption for you here:

Plate XIII.

A SOLDIER WITH HIS MATCHLOCK.

The military of China differs, as every thing else differs, from that of all other nations, in the nature of its establishment, its occupation, and its dress. They have two distinct armies, if they may be so called; the one composed entirely of Tartars, who are stationed in the several provinces on the Tartar frontier, and occupy all the garrison towns of the empire; the other composed of Chinese, who are parcelled out in the smaller towns and hamlets to keep the peace, by acting as constables, subordinate collectors of the taxes, guards to the granaries, and assisting in various ways the civil magistrate. Along the public roads, canals and rivers, are placed, at certain intervals, small square guard-houses, at which are stationed from six to twelve men, who are employed in settling disputes upon the rivers or roads, and also in conveying the public dispatches. When a foreign ambassador or any of their own mandarins travel, these soldiers turn out in their holiday dresses with their streamers stuck in the back, as in the annexed figure. The breast-plate and shoulder-guards are nothing more than cotton stuffed with wadding, and the helmet, which looks so fierce, is made only of paste-board. The Chinese matchlocks resemble so much the old common matchlock of the Portuguese, that it has been supposed these people first introduced them into China, where however it is sufficiently determined, gunpowder was in familiar use many centuries before any communication was known to exist between this country and Europe. In some of the larger matchlocks there is a fork to support the piece, and by sticking it in the ground to give it the degree elevation that may be required.

What Alexander's description tells us is that this is a Han Chinese soldier of the Green Standard Army, turning out in ceremonial rather than service dress. The various bits of seemingly steel armour are just padded cotton emulating some of the appearance of earlier lamellar armour styles, while the helmet is supposedly just papier-mache. A Banner soldier might still be issued with a steel helmet into the mid-nineteenth century, but for the most part metal body armour had gone out of use by the time that Alexander was drawing his illustrations and writing his (decidedly prejudiced) captions. A more typical appearance for a musketeer or indeed any Qing soldier, also taken from Alexander's illustrations (this time the 1805 edition of The Costume of China) would be something like this or this.

Alexander does tend to exaggerate and exoticise, though: this Qing-era training manual, the bingji zhizhang tushuo 兵技指掌圖說 ('Illustrated Handbook of Military Techniques'), shows a more conventional sort of military dress, with one variant including a padded vest and short tunic, and another with an ankle-length robe and eschewing the vest. Note, in this case, that the troops being depicted are Manchus, unlike the Han troops Alexander was depicting in the two examples I linked at the end of the last paragraph – the key difference is in the tunic and vests, which for Manchus buttoned down the side rather than the front.

In short, then, metal armour was decidedly out of use by the time Alexander visited China in 1793, and he himself does not say that he saw people wearing it.

If you want to check out Alexander's illustrations (but, uh, skip the text unless you want to be scarred by all the racism), the 1814 edition can be found here via Project Gutenberg, and the 1805 edition here on Wikisource.