Although English historians have defined Reich as being a strictly German concept of sovereign rule, in the German language itself it means "Empire". In English, we speak of the Holy Roman Empire; in German, it is the HRR or "Heiliges Römisches Reich Deutscher Nation".
Wiktionary quotes Busching, who in 1762 explained Reich as a German understanding of "Eminence", from the Latin Regnum, rather than an Empire or a Realm as other cultures would understand it.
One could see it as a word used in English, Russian, Portuguese and many other languages as a designation for any kind of German kingdom, empire or absolutism, similar to how one would address a foreigner according to their origin, e.g. Senor Martinez, Monsieur Aragon.
Compare it to how many cultures, including the Germans, also use the word "Commonwealth" or "Soviet Union", despite the fact that Bavaria had formed its own Union of Soviets, the Räterepublik, during the Weimar Republic.
If you're interested in knowing when the word "Third Reich" came into usage, it is worth noting that during Fascist Germany, the country's official name was Das Deutsche Reich, and in the USA and UK it was usually referred to as Germany, Hitler's Germany, Berlin, Reich or, the most popular term, Nazi Germany.
(Sources: Neville Chamberlain's declaration of war against Germany, headlines about Germany in newspapers like the NY Times or the Times, the Daily Mail's Lord Rothermere)
In Germany itself, the idea of a third Reich stemmed from the 19th century, where it was a popular philosophical theme in literature and theology. Writers like Johannes Schlaf, who wrote "Das Dritte Reich" in 1899, or the German translator of Ibsen's "The Emperor and the Galilean", popularized the idea of the imminent arrival of a thousand years of Christianity (a kind of positive apocalypse), which would follow a third "Reich". And they would quote Paul the Apostle and various saints, to make it clear that the third Reich would follow the heretic lex naturalis and the lex mosaica.
Nazi propagandists exploited this in their articles, making it sound as if the saints had had some sort of epiphany about Hitler and the Nazis.
In other words, the Third Reich began as an abstract idea of a Christian revolution, but was assumed by Nazi writers in order to bolster Hitler's popularity and justify the drastic and bloody decisions that the Fascist government was making.
In one of the earliest examples of the Third Reich being mentioned outside of Germany, Major Strasser in the film Casablanca talks about the Third Reich as if it was just the beginning to a kind of paradisaical future or of a fourth Reich.
After 1945, the term was used exclusively to associate only to the unsuccessful reign of Fascism in Germany, and it ceased as a philosophical or theological idea in German literary circles.