So the Japanese words for newer concepts or objects are often Western words pronounced in a Japanese way, like コンピューター (Konpyūtā) for computer, so was kissing a modern concept?
No. There are other words in Korean for kiss such as, 뽀뽀(Popo), or 입맞춤(IpMatChoom). Older generations use these words, while younger generations use "kiss". I can't give you an answer why, but I would assume that televisions, dramas, and foreign movies has had an impact on it as "kiss" is sort of seen more as stylish.
It's worth mentioning that the common words for "sex" (i.e., sexual intercourse) in Japanese are now "セックス" (sekkusu) and " エッチ" (ecchi). The first is a direct transliteration from English. The second is a back-formation of interesting origin: the word for "perversion" or "lewdness" in Japanese is "hentai." Hentai has entered the lexicon of English as a word for Japanese pornography (usually manga or anime). "Hentai" in English starts with the letter "h." The way to pronounce that letter in Japanese is "ecchi." The Japanese have adopted the English pronunciation of the first letter of the romanized version of their word for "perversion" to fill this role.
So, both commonly used words for sex are now directly derived from English, but it can be considered pretty certain that Japanese people were having sex long before these terms came about. (In point of fact, the word "性交" is still sometimes used, but it is considered slightly archaic).
This whole thing is part of a larger movement in Japanese, and to a lesser extent, Korean, of English words replacing their original counterparts. This is particularly true of words associated with risque or lurid things, or with words that younger people are likely to use -- both of which kissing and sex qualify under.
This article discusses the etymology of 키스: http://www.korean.go.kr/nkview/nknews/200501/78_1.html .
It first appeared in print in 1922 in a novel titled 젊은이의 시절 which is apparently still in print. Also 흙 which was made into a film.