I presume that it makes a difference legally. You can't use it as evidence in court (for future court cases perhaps) if you're not legally allowed to have it.
I suspect you're right. Can one, however, be compelled legally to delete a copy of a downloaded video that you were legally allowed to download?
I suspect, therefore, that it will have legal standing that it will not be allowed in court, and it will be illegal to distribute the video, but I feel as though you can't legally compel me to delete it.
Of course, I'm not a lawyer, but I could encrypt the video such that you could never prove I had it.
Wrt the judge/legal process - I wonder what will happen when it turns out that the footage can't be removed. I could see the fact that it can't really be removed being used against KimDotCom by showing something like "the irreparable" harm he did by allowing users to basically upload pirated content that would never truly disappear. So maybe the judge is clever and giving KimDotCom just enough rope to hang himself with?
That was a quote from a photo caption in the news article, not the judge nor the decision (which I cannot find online). It's unlikely the judge was actually under this sort of misconception. (If you have a link to the decision text and it shows otherwise, I'll stand corrected.)
He must follow the media laws, which means that the stream to the public must be live and not a recording. The order is for Kim Dotcom to stop making the stream available once the hearing ends.
If a third-party makes a copy, its not Kim Dotcoms fault in the same way that TV stations are not charged with a crime if someone makes a copy of the news which includes live footage. At worst, the "media" entity is responsible to behave professional and act according to some best practice, but those kind of liability requirement tend to have a high bar.
The judge obviously doesn't know how the Internet works, but I applaud his efforts.