I’d say that they are partly right with this assertion:

I don’t think it is appropriate to speak of medieval for cultures in whose historical discourse on periodization the concept of a medieval period is not established.

After all, it’s just a word we made up to describe a span of time situated within a linear arrangement of such timespans (i.e., periods), and that ascribes to this timespan certain characteristics, which differentiates it from those coming before and after. Typically, the medieval period is characterized as being more diffuse and decentralized than the sprawling empires of yore and the modern nation states. (See also, for example, the evil F-word which often is used synonymous with "medieval.")

The most basic idea of such periodization is a tripartite division into a classical or antique era and the modern era, with the medieval being “that period in-between.” Of course, things became way more complicated nowadays, with endless subdivisions and debates on which is starting when (because historians love arguing about this kind of stuff), and the discovery of rather fuzzy borders: historical phenomena tend to linger around, and not just conveniently go “poof” all at the same time.

Anyway,

Certainly, these kinds of periodizations, and with them the “medieval” period, were developed by Europeans in the study of European history. I suppose that makes it eligible for being an inherently “Eurocentric” idea; however, as all the other more-or-less-wise things written by Europeans, it has been studied—and sometimes adapted—by historians of other cultures.

As far as I know, Japan is the only nation which actually “discovered” a medieval period which more-or-less coincides with the idea of the European medieval, and fitted into an argument of a development from centralized to decentralized and back to a centralized state. That this happened in a time of enforced modernization, the era of imperialism and colonization, and the wish to be perceived as being on par with the Western colonial powers is, maybe, just mere coincidence (1).

On the other hand, if you’d actually want to find a “medieval” period in, for example, China, you’d apparently end up with a period before the Han dynasty: a chunk of the first millennium BCE, and possibly even earlier than this (it appears that the idea of medieval China has not garnered much support).

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In short:

Not only Europe uses the idea of a medieval period.

However, the time spans covered by these medieval periods (plural!) are not conveniently the same everywhere. Therefore, the proper term for artifacts and buildings from areas where a medieval period is not established in its historiography would be whatever terms you have available in the respective periodization system.

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(1): The first Japanese historian to introduce “medieval” into the historiographical discourse was Hara Katsurō, in 1906’s Nihon chūseishi. Originally, the medieval period was rather neatly defined to begin with the establishment of shogunate government, until the beginnings of reunification in the late 16th century; so, 1185–1573. Alternative propositions have since become dominant, some seeing the beginning of the Japanese medieval in as early as the 9th century.