I tried running the GIF backwards to see how he constructed the puzzle but that didn't work so I started thinking about it.
The wire is easy. A thread threaded through the hole in the cigar and lightly glued to the end of the wire could be used to guide it through the hole, after which the glue is melted/dissolved/torn and the thread removed.
Getting the bolt in the hole in the cigar could be done in a similar fashion.
However, putting the nut on the bolt has me stumped. Perhaps hold the nut stationary with a magnet located outside the bottle and rotate the bolt into it using another thread wrapped around the bolt. Seems too tricky, though.
What do the experts say?
On reflection, the nut could be strung on the thread that pulls the bolt into the hole. This would help guide it into position and then perhaps allow the ball to wind the nut onto the bolt in a manner similar to the way the ball is used to unwind the nut in the solution.

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