Of course, it would be foolish to assume that everyone who likes anime and manga automatically loves video games. However, in the interest of being topical, it isn't foolish to realise there is a substantial overlap between those who enjoy anime and manga and those who enjoy video games.
During the '80s, those who made an unfortunate choice may have enjoyed watching recorded anime on Betamax. While the term Betamax is of Japanese origin, it is a proprietary name invented in the dark recesses of a marketing meeting.
The otaku movement is considered to have been born at the same time as the anime boom following the popularity of anime shows such as Mobile Suit Gundam, which features fine examples of mecha (メカ), an abbreviation of the word "mechanical". Technically, as an abbreviation of mechanical, the term mecha is an abbreviation of an English loanword which has its own roots in Greek and Latin.
Of course, Japan's history with martial arts means that the word dojo is known by most people who watch anime and read manga. They are fully aware that if you are in a dojo, you should get ready to practice some martial arts, particularly judo.
This exchange of nerdiness in Japanese culture obviously lends itself to the internet. The word emoji comes from the Japanese for "picture", e, and moji, meaning "letter" or "character". It does seem that this word is becoming more popular than the term "emoticon", from the English words "emotion" and "icon".
When you have this cross-pollination of anime, Japanese culture, and the internet, you inevitably get the type of content the internet is rife with, porn. The term hentai refers to pornographic anime and while we won't include pictures, if you are really interested in finding out what it is, a quick search will yield more results than you ever wanted to see.
A word we keep hearing more and more in spoken English is the word kawaii. The Japanese term for "cute" is often used to describe Japanese things that are cute, but is increasingly used by gaijin (the Japanese term for foreigners) for non-Japanese things that are also cute.
A Japanese word that hasn't quite made its way into popular use is hikikomori. However, the Japanese term for shut-in, recluse, or someone who will attempt to avoid any type of social contact, is growing in popularity as sadly, the issue is becoming more and more common in contemporary Japan.
However, while I have painted a picture of a one-directional linguistic relationship with Japan, this is barely the case. There are also otaku words of English origin that have made their way into Japanese, such as fan fiction (ファン フィクション) and fan service, (ファンサービス), to give a couple examples.