Edit: Looks like you updated the link to a new page (was abstraction of potential realizability, is now the abstraction of actual infinity). I will take a look and see how that changes my answer below.
Edit 2: I don't think the link update really changes the general ideas in my response below. The first link was about disregarding that reaching infinity is not doable in practice when assessing the validity of conclusions, whereas the second is saying, pretend it is actually reachable and treat it as if it has been reached. The ideas are similar. I'm not planning to modify my response further.
In the same encyclopedia website, searching for the law of the excluded middle, there is a section that says:
Since there is no general method for establishing in a finite number of steps the truth of an arbitrary statement, or of that of its negation, the law of the excluded middle was subjected to criticism by representatives of the intuitionistic and constructive directions in the foundations of mathematics (cf. Intuitionism; Constructive mathematics).
I think the connection is this finite steps idea. By embracing the abstraction of potential realizability, one accepts unbounded constructions as valid, even if it would be impossible to physically carry out an infinite number of logical steps or calculations. Applied to the law of the excluded middle, a given proposition may require an infinite number of steps to establish it's truth or that of its negation. The abstraction of potential realizability essentially says that you can treat things that require an infinite number of steps as valid.
This reminds me of something I read in the book Gödel, Escher, Bach, which I highly recommend. It explains how Gödel's incompleteness theorem involves the construction of statements that essentially say "This statement is not provable within this logical system". It is analogous to the "this statement is a lie" paradox. At the end of the book, there is discussion about adding an axiom to state a proof to the paradoxical statement does exist. By doing so, one finds that such a proof is essentially infinitely long (contains an infinite number of deduction steps). Incidentally this then implies the existence of a whole new class of numbers called surreal numbers, which is pretty interesting. The relevance here is: there was a paradoxical proposition that seemed neither true nor false, apparently falling within the excluded middle zone. By asserting there is an answer, one can resolve the paradox (placing the proposition squarely in either the true or false realm), but doing so requires acceptance of logical arguments which are infinitely long, embracing the abstraction of potential realizability.