As everyone else said those are not khevsur swords but western georgian imereti to be specific, and it was mostly nobility weapon used from horse back, in other words a cavalry sword which may explain the reason for the shape and the angle between the hilt and the blade.
I don't how much you know about using swords from horse back but basically it is about pointing your sword at the target "if you are going for a thrust" or lining your sword blade with the target "if you are going for a cut" moments before it reaches it and the power source for the attack would be the speed of the horse, so if we leave cutting for a side and focus on thrusting, being on a horse means you are higher than your target with a normal hilt that is in line with the blade you may need to bend your wrist to do the thrust but the problem with that is you may injure your wrist which is not something you would like to happen while fighting, with an angle similar to this you can keep your wrist in more straight with your arm which could prevent or reduce your injury, at least that is what I think.
We also see similar angle between hilts and blades in swords used by nomadic people wich used swords from horse back, and that is why I think that is the reason for such sword design
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