Addendum
The word 時{とき} is probably the oldest native Japanese word for "time". This term appears in the 万葉集{まんようしゅう} written in Old Japanese and compiled from poems composed from the 300s through the 700s, completed some time after 759 CE. These are some of the oldest surviving examples of written Japanese, suggesting that this term is quite ancient indeed. Consequently, claiming that ancient Japanese had no word for "time" is patently wrong.
The Japanese language also has the Chinese-derived on'yomi term 時刻{じこく}, also used to refer more specifically to the concept of "hour", as in "a specific length of time in a day". This term appears in the 平家{へいけ}物語{ものがたり} dating to the 1100s. Even prior to that, we know that the Ritsuryō legal system in place from the mid 600s through the Nara period ending 794 made use of water clocks to track the passage of time during a day: definite evidence of the Zeitmessung ("time measurement") that Professor Geißler mentions. In the traditional reckoning, each day consisted of 12 hours: 6 of day, and 6 of night. This meant that the length of a daylight hour and of a nighttime hour changed over the course of the year, with the shift of the seasons. Consequently, an argument could be made that the traditional Japanese hour required a greater awareness of time than the western hour -- timekeepers would need to be much more intimately in tune with time day-by-day in order to evenly distribute the number of hours in a day and night.
Even the western definition of "hour" has been known to some extent in Japan since the 1500s, when westerners brought their own clocks as gifts. So here too, Professor Geißler's claim falls through.
The term 時間{じかん} itself, though apparently extant earlier, does seem to have been repurposed in 1881 as a specific translation of the western term "time" in reference to philosophy. The Daijirin entry here explains:
〔明治初期には英語 time は「時・時刻」と訳され、「哲学字彙」（1881年）に訳語として「時間」と載る〕
(The English term "time" was translated as 時{とき} or 時刻{じこく} at the start of the Meiji period [beginning 1868; here, likely including the 1870s], with the term 時間{じかん} appearing as a translation term in Tetsugaku Jii (1881) ["Philosophical Dictionary", compiled by Inoue Tetsujirō])
Notably, most (maybe all?) such "translation terms" were existing words in Japanese that were repurposed to express more western concepts, such as 社会{しゃかい} "society", or 自由{じゆう} "freedom, liberty".
Key points:
- The concept of "time" clearly existed even in ancient Japanese culture.
- The concept of "hour" as a specific span of time has also existed, for essentially the entirety of recorded Japanese history. Granted, that definition might have differed from the modern western concept, but it was a specific idea of "time measurement".
- The main shifts related to "time" in the Meiji period were:
- widespread translation of western materials in an urgent and strategic push to catch up technologically, leading to the rejiggering of various cultural ideas, including "time", and
- the promulgation of the Gregorian calendar and western-style 24-hour day, as opposed to the traditional 12-hour day, with six hours of day and six hours of night.
Conclusion
You had specifically asked:
Is it true that there was no word for time before the Meiji restauration?
No, that is not true.
What word is he [Professor Geißler] referring to? 時間 or the kanji 時?
Professor Geißler is far enough off-base that I don't think he's referring to any specific term -- I suspect he doesn't know enough about Japanese history or the language for either term to be immediately relevant to his statement.
Professor Geißler clearly got the wrong end of the stick. I note that he is apparently a Professor of Wirtschaftspädagogik, or "economics pedagogy", with no apparent work in Japanese history, culture, or language. In his defense, it is easy to misapprehend things outside of one's field of expertise.
