How come What does this paper claims to have solvedto do with Hilbert's fifth question?

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asked Aug 26, 2020 at 12:24

How come this paper claims to have solved Hilbert's fifth question?

Apparently, there is a paper

M. Sablik, Final part of the answer to a Hilbert's question. Functional Equations - Results and Advances. Edited by Z. Daróczy and Zs. Páles, Kluwer Academic Publishers 2002, 231-242.

however I struggle to understand what does it have to do with Lie groups and Hilbert's fifth problem. Is it something deeper I fail to see here?