What is the meaning of scores when comparing reaction classes in the KEGG database
And does [the score] signify the bonding strength of how probably it is for a pair of compounds to be an R pair?


No, it has nothing to do with that. It is not about how probably a particular reaction is.

When comparing RCs (reaction classes), the scores in the table of related reaction classes are just a measure on how similar these reactions are. 

RC00064 apparently is an N-acylation or the formation of a peptide bond. RC00197 with a score of 1.0 is a N-formylation and considered very similar.

Change the cutoff to a lower value, such as 0.4, and compare the results at the end of the table with RC00064. You'll find dissimilar reaction classes like RC02518, the oxidation of a selenol to a selenic acid.