What is the origin of cheese dip?
If we're going to define "cheese dip" as "some substance made from cheese for the purpose of dipping other food in" - which seems like the only rational definition given no other context - then I'd have to pinpoint its origin as being fondue.

According to Wikipedia, the earliest known recipe for fondue comes from the Swiss cookbook, Kochbuch von Anna Margaretha Gessnerin, ein gebohrne Kittin, first published in 1699.

That predates the Arkansas claim of 1935 by at least a few centuries, if we assume that Wikipedia does indeed list the earliest source.

There's also Queso Chihuahua which was supposedly brought to Mexico by the Mennonites, which would place its origin in Mexico sometime in the 1920s - assuming that the Mennonites themselves did not simply adapt the recipe from something known even earlier.

I'd have to say that the Arkansas tourism board seems to be trying to pull a fast one on us, laying claim to this "invention". Maybe they're defining cheese dip as the specific kind of cheese dip they came up with, which would of course be a tautology.