Actually, there’s a variety of sword widths found historically, including some really fat longswords and broadswords.
I hate using Wikipedia as a source but it’s got some info on a system used to label swords in their variations of length/width ratio, with plenty of the Viking and Celtic swords being thicker.
It is true that Tusk’s sword seems a bit exaggerated, but it’s really just an upscale version of swords that already exist. Most big swords seemed relatively thin, even if you take into account their actual thickness (I’ve got a 2 handed display sword about as thick as my arm that we got from a catalog a while back, but you can’t tell since its as tall as I am) because making a large, thick sword would be very taxing on a real human. However, seeing as Tusk is not only a Killer Instinct character but also a man who’s hardy enough to be standing around shirtless in the middle of the artic with back muscles the size of a small bear, I think it can be forgiven if the sword is bulkier than a realistic sword.
Though, there are real swords that dwarf Tusk himself size. If I remember right, there was a Scott named Maxwell born with gigantism who wielded a claymore that was 7 1/2 feet in length.
On topic: God I love Tusk GIFs.