No, that is about a court re-trying someone, which they cannot do. The evidence itself may well prove their guilt.

The point being that a lack of evidence of guilt is not evidence of a lack of guilt. But we require evidence of guilt for convictions, not a lack of evidence of innocence (in criminal cases, and if it's not an affirmative defense).

If they have been found not guilty (given) when exactly is this newly found evidence going to convict? That’s the point of double jeopardy.

It didn't say "convict", it said "prove". Evidence can prove someone guilty even if a court is unable to do anything about it.