I think the idea is, suppose you have an oracle which tells you if a Turning machine will halt, in finite time. There will still halting problems for that oracle system, which requires an oracle from a higher level system. (That is how I interpret "an oracle that magically gives you the answer to the halting problem for a lower number of interleavings will have its own halting problem it cannot decide in higher numbers of interleavings").
This appears to discuss it a bit more. Not certain if it's more helpful than the comment (still going through it), but it does cover it more in detail.
mtg is more recent than things like the johnniac, but plausibly there's a traditional card game with the same criteria that predates electronic computation
but then we have to ask thorny ontological questions: does a card game count if it requires a particular configuration to be turing-complete, but nobody ever played it in that configuration? what if nobody ever played the game at all? what if nobody even knew the rules?
The MtG preprint suggest people have been looking for such games but failed to identify any. From "Previous Work", first page, column 2:
> Prior to this work, no undecidable real games were known to exist. Demaine and Hearn (2009) [10] note that almost every real-world game is trivially decidable, as they produce game trees with only computable paths. They further note that Rengo Kriegspiel {Rengo Kriegspiel is a combination of two variations on Go: Rengo, in
which two players play on a team alternating turns, and Shadow Go, in which
players are only able to see their own moves.} is “a game humans play that is not obviously decidable; we are not aware of any other such game.” It is conjectured by Auger and Teytaud (2012) [1] that Rengo Kriegspiel is in fact undecidable, and it is posed as an open problem to demonstrate any real game that is undecidable.
> The approach of embedding a Turing machine inside a game directly is generally not considered to be feasible for real-world games [10].
Regarding your ontological question, that we don't know if something is Turning complete doesn't mean it isn't.
People explored the Game of Life before it was proven to be Turing complete. The 1970 SciAm article says "Conway conjectures that no pattern can grow without limit." so Martin and Gardner didn't even know about gliders then. People don't say GoL wasn't Turning complete in 1970.
I pointed to a 1998 paper claiming the Z3 machine from the 1940s was Turing complete, that author clearly believes that a particular physical configuration is not required.
Nor did Turing construct a physical representation for his paper.
FWIW, the MtG preprint gives a concrete example of a 60-card initial deck. I would be surprised if neither the authors nor anyone else has ever tried it.
The ontological question is even more fully resolved because no one has ever created a real Turing machine. We always have the proviso "if given enough memory".
i don't have much to add here but wanted to express my gratitude for having had the opportunity to read your wonderful comment
well, maybe one thing: if it doesn't matter whether anyone played the game or knew the rules, then magic: the gathering was turing-complete before the first magic deck was printed, before the first human was born, before the first star was formed, perhaps before the big bang
If you go down that route you'll realize there are an uncountable number of games that have never been created, and will never be created, which are Turing-complete.
And start wondering if mathematics is created or discovered.