There's not really any difference, but you changed the negation. In the original French sentence, the entire subclause is negated and this is also the case in the professional translation. In your translation, you shifted the negation from the entire subclause to just the verb of the subclause.
If you do the same thing to the negation in the original sentence, you would get:
- Connectez les points pour que les chemins ne se chevauchent pas!
- Connect the dots so that paths don't overlap!
- Connectez les points sans que les chemins ne se chevauchent!
- Connect the points without the paths overlapping!
You can probably see how they are different. The subclause is positive in your version, and negative in the other. This can lead to different interpretations.
If you negate the entire subclause, the sentence will be interpreted as:
Connect the dots in any way; as long as the paths don't overlap it's good.
Whereas the sentence you made can be interpreted as:
Connect the dots in that specific way where the paths don't overlap.
The difference in meaning probably doesn't matter, because I'm guessing there probably is only one way to make the dots connect without the paths overlapping. Nevertheless, there is a difference in meaning and when translating short, specific sentences you always want to translate faithfully and express the exact same meaning in the target text as the original sentence conveys in the source language.