I'd agree with Wikipedia. After all, there are plenty of other physically-realizable models of computation that are equivalent to Turing machines in terms of what they can compute but substantially inequivalent in terms of how long it takes.

[EDITED to add:] ... Though I think anything you can do in a Newtonian universe can be modelled on a Turing machine with at worst a polynomial-in-problem-size slowdown. So there might be something to be said for counting as "hypercomputation" anything that, e.g., can evaluate all computable functions in constant time. But that isn't the usual use of the term.