Is there a certain level of Japanese language skills required?

Most definitely not! They encourage you to not speak any Japanese with your students even if you do know it. I speak no Japanese at all and was able to communicate with my students no matter what their age was. The course teachers teach you how to do this.

There are no Japanese language skills required for ITTT TEFL. You're undergoing training to teach them English from a Western culture's perspective. Although it would be beneficial to have some kind of effective way to communicate your point across to the Japanese students. So, understanding of Japanese language and culture will only help you.

No Japanese is required. It's handy to know, especially as very few
sober Japanese people will be willing to talk in English (for some
reason their language skills magically appear when they are drunk).
The only language needed for the course is English. Experience with a
different language is a good thing, as it is easier to empathize with
ones students. That being said, it is by no means needed and most of
the people taking the course while I was there only knew English.

It's not necessary to know Japanese for the course. Knowing some Japanese will make the stay in Japan more comfortable.