"A value in Hoon is called a noun" - or you could just call it a value.
"A gate is a Hoon function" - or you could just call it a function.
"A core has no exact equivalent in conventional languages, but the closest equivalent is an object. An object has methods; a core has functionally computed attributes (arms). An arm that produces a gate is the Hoon equivalent of a conventional method;" - or you could just say that objects in Hoon (the language) can have methods and attributes, and you would never need to invent the core/arm/gate terminology.
They try to give themselves an out by saying stuff like "Hoon has concepts like all these abstractions, but they remain false cognates." When you dig into it, the only unique things are the words. It's like children trying to come up with a code- "instead of door we'll say blorp and instead of close we'll say bleep. Now bleep the blorp before we continue inventing our code.