It’s not surprising—there’s a deep relationship among concatenative languages, Hughes’ arrows, combinator calculus, category theory, linear algebra, logic, even topology. I haven’t read through this but I guess the ⊕ operator would be “* * *” (parallel composition) in arrow notation; in Haskell it has the type “Arrow a ⇒ a b c → a b′ c′ → a (b, b′) (c, c′)”, or “(b → c) → (b′ → c′) → (b, b′) → (c, c′)” specialised to the function arrow.

There's no operator because composition and direct sum are implicit in the order of your program words.