This phenomenon is fairly common, and can be called "semantic change" or more specifically "semantic narrowing". It is one of many patterns that crop up when a word is imported from one language to another.
Using sake for the fermented rice drink reflects the fact that it is a drink that English-speaking people had not previously encountered. It is one of the earliest words to be received into English from Japanese - the OED traces it to 1687, in an English translation of a French traveller's book (The travels of monsieur de Thévenot into the Levant):
Their ordinary drink is a kind of Beer (which they call Saque) made of Rice.
From the citations there, it seems that sake in English has consistently meant the same thing since its original borrowing.
The Japanese contributions to the English language: an historical dictionary (Garland Cannon, 1996) suggests that British travellers in this period "generally showed little interest in learning Japanese" and that although they ate the local food, they would typically speak and write of it using English words. Consequently, the Japanese words would tend to be applied for foods (or other things) that had no clear Western equivalent, or were in some way distinctively Japanese.
Example borrowings from the same period include food words like miso and soy, political terms like daimyo and shogun, and names for Japanese plants, furniture, swords (katana), clothing (kimono), and so on.