If you look at the fork yokes for the Gixer - you will see that the fork tubes are very close to the steering stem.....there is very little offset.
The Savage on the other hand has a very significant offset, and the fork tubes are significantly forward in the yokes.
When I was building my Cafe', I used yokes from a Suzuki RM250, as the fork tubes were the same diameter and top yoke had a clamp that would allow me to drop the tubes to lower the front end without installing the RYCA spacers that limit fork travel. It seemed like a good idea at the time - however it affected the steering in a very bad way.......reducing the offset increases the trail, and makes the bike steer like a truck! It tracked fine and went around corners well - but when you got to a corner and needed to turn....the bike took a large amount of pressure on the handlebars to get the turn started. MMRanch rode my bike and when he got off he said that entering the turns - "Felt like he was trying to bend a board!".
Here is a photo that shows the stock yoke and the RM250 yoke.
The sport bikes have much steeper fork angles and work great with the small offset - the Savage with the cruiser styling and shallower fork angle needs the larger offset to steer well - and I would expect that using the GIXXER fork yokes without changing the angle of the steering head is going to make for a very stiff steering motorcycle.
The "custom" Savage that you linked is most likely pushed around a lot to get to the shows......and they may actually never ride it (it doesn't have a license plate, turns signals, mirrors or any noticeable wear on the tires). I would love to see a Motorcycle magazine do road tests on some of these "show bikes", and comment on how well they do (or likely don't) ride.