「非常に大きな」接頭辞gigaはgの音で始まる「ギガ」だけでなくjの音で始まる「ジゴ」とも発音

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ではこの jigowatt （ジゴワット）、まず第一に実在する単位なのでしょうか。

答えはＹＥＳです。

ただし、綴りは jigowatt ではなく、gigawatt。え、giga は 「ギガ」 と発音するんじゃないの、という反論もあるでしょう。しかしこの 「非常に大きな」 という意味を持つ接頭辞 giga は g の音で始まる 「ギガ」 だけでなく j の音で始まる 「ジゴ」 とも発音されるのです。（Merriam-Webster Online 辞書参照）

「非常に大きな」接頭辞gigaはgの音で始まる「ギガ」だけでなくjの音で始まる「ジゴ」とも発音
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http://mw1.merriam-webster.com/dictionary/giga
Definition of giga- - Merriam-Webster Online Dictionary
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Bob Gale: I should talk about "jigowatts" for a second. The proper pronunciation, of course, is "gigawatts" [with a hard "G" sound], and when Bob [Zemeckis] and I were doing research, we talked to somebody who mispronounced it "jigowatts". We were actually completely unfamiliar with the term, and we thought that was how it was supposed to be said. It does come from the Greek 'gigas' [that Greek root is pronounced with a "J" sound, not a "G" sound], for gigantic, so I suppose it's not beyond the realm of possibility. But never having heard of it, we actually spelled it in the script "jigowatt". A "jiggowatt" is actually supposed to be a gigawatt, a million watts. So the mystery of the gigawatts is now solved.

[NOTE: Bob Gale made a mistake here, it should be "billion" rather than "million"!]

pronunciation, of course, is "gigawatts
pronunciation　gigawatt
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Popular culture
The soft g pronunciation of gigawatt (i.e. [ˈdʒɪgəˌwɑt], JIGA-wot) was used in the Back to the Future movies. This usage predated the common occurrence of gigabytes and gigahertz in common American usage.

発音付の American Heritage Dictionary で発音させてみるとジガワットと聞こえます。