I don't want to scare kmf off from coming here; you should, it's a wonderful country. Just need to manage your expectations...
You should certainly learn Japanese if you want to live there, but you'd still be way better off than rural Russia.
I see hudibras is getting downvoted but it probably is fair to say that to native English speakers new to the country, people may expect more than they get from ESLs in Japan. I have some pet theories as to why but I don't think it would contribute all that much to the discussion. Unless you're coming to Japan to be a corporate translator (may all the gods have mercy on your soul) it really shouldn't be an issue as long as you're willing to learn a little Japanese along the way.
Shopping in Korean, I can just set it to OCR mode and sorta read labels I don't understand. (Of course, Hangul's probably a lot easier to OCR than kana+kanji.) I've also found that while the store people will respond to me in Korean if they don't see me, once they realize it's me they flip into a common third tongue.
I've even had "conversations" in other languages just by pressing the flip button and letting the other person talk. They can correct any audio recognition failures or just type.
In general, the translations for simple stuff and interactions seem pretty good. Sometimes you need the alternative translations to find one that is accurate. But I wouldn't say you "cannot speak, listen, write, or read anything".
OTOH, sometimes it has odd things. Formal-something I (吾輩) like from the "I am a cat" gets translated as "Spence" (I think the pronoun isn't used much). Or maybe one possible pronunciation of them is close enough to Spence it's used as a name in some place that uses those characters?
Not to mention, you can pick up the kana in a week, and at least the meanings of the basic kanji in a month or two, claims the guy that made the book that did teach me kana in a week. I'd assume if you're gonna go to Japan and be serious, you'd at least listen to the first 10 Pimsleur sessions for basic "hi I can't speak Japanese", and learn the scripts somewhat.
For a job interview or a more formal business environment though, you're going to start at a considerable disadvantage if you don't speak Japanese in Japan. It's possible (I did it), but it's really, really hard.
I always say that the true test of being fluent in Japanese is not being able to read the newspaper or have a conversation. It's being able to read and fill out a government form while people are waiting in line behind you and a bureaucrat is waiting patiently in front of you.
If one goes strictly by the published requirements, it would not be straightforward to get you an engineering status of residence (so that you could be hired as an engineer by a Japanese company, as opposed to being transferred in from a foreign company), but there are ways around that. (For example, documenting that you have 10 years of paid experience in development would satisfy the degree requirement... that documentation will be expected with to-the-month resolution.) Candidly, if you do not speak Japanese, getting a professional job with a Japanese megacorp is likely to be quite difficult. (There are a very few prominent exceptions, such as Rakuten.)
There are some Japanese startups which hire foreigners who do not speak Japanese. Your best bet for getting hired at one is to know the decisionmakers personally (true of getting hired at any company anywhere, but of particular interest to you). One potential avenue for finessing this is to come to Tokyo on a visa-waiver for a few weeks of sightseeing, meet people like it is your job, and then get the ball rolling on employment. Fair warning: many startups are, like the US, not exactly organizationally optimized to support your visa/status of residence paperwork.