That's basically Platonism. I think it's a reasonable position for some things, e.g. Booleans (two-valued logic), natural/integer/rational numbers, tuples, lists, binary trees, etc. I think it's meaningful to talk about, say, the number 2, separately from the way it may be encoded in RAM as a model of e.g. the number of items in a user's shopping cart.
This position gets less reasonable/interesting/useful as we consider data whose properties are more arbitrary and less "natural"; e.g. there's not much point separating the "essence" of an IEEE754 double-precision float from its representation in RAM; or pontificating about the fundamental nature of a InternalFrameInternalFrameTitlePaneInternalFrameTitlePaneMaximizeButtonWindowNotFocusedState[0]
The question in the article is whether lambda calculus is "natural" enough to be usefully Platonic. It's certainly a better candidate than, say, Javascript; although I have a soft spot for combinatory logic (which the author has also created a binary encoding for; although its self-interpreter is slightly larger), and alternatives like concatenative languages, linear combinators (which seem closer to physics), etc.
[0] https://web.archive.org/web/20160818035145/http://www.javafi...
In Plato's allegory of the cave, this was the true monster casting shadows on the wall.