The translation on the video is correct, it means "that's great! / how great!" with emotion/exclamation. すごい is an adjective and it has several meaning depends on the situation. (great, amazing, awesome / heavy, enormous / awful, horrible, terrible) *すごく is an adverb. This じゃない express the exclamation and if the tone of the voice is like ⤴︎, it means "that's great, isn't it?". *the simple negative form of the adjective すごい is すごくない, not すごいじゃない. じゃない is the negative form for NA-adjective and some which end with だ, like 元気じゃない、わたしの本じゃない. However, depends on the tone of the voice, the meaning is changed to "that's my book!", "that's my book, isn't it?", "that isn't my book". I hope it was helpful.

Yeah you are right, sugoi is amazing and jya nai is negative. The only logical explanation is to notice the tone being used by the speaker, I think it may be something like " isn't it amazing?" (This would make more sense if speaker says すごい じゃ ない か