How to retrieve logical expression (KO based) for reactions from KEGG?
To rephrase what you already mentioned in your question: For a KEGG Module to be completed (so that an organism can perform a certain function) you need a certain set of functional units or enzymes. So to evaluate the abilities of an organism you would check its genome for the gene sequences related to the module by performing the logical operation you mentioned above.

A Module is composed of chemicals (C) and reactions (R), as you can see in your given example. To explain the differences between modules and reactions best have a look at the last reaction, Isocitrate to 2-Oxoglutarate. There are three boxed reactions (one of them is a combination of two) that all lead to Oxoglutarate. When you look at the Orthology (the enzymes involved) for the reactions in the first box (R01899+R00268) and the second box (R00267) you will see, that it's the same enzyme (K0030) performing different reactions. The third box now contains a reaction (R00709) performed by a second enzyme (K0031), that leads the same way (it differs in using NAD+ instead of NADP+ as electron acceptor). So for the module to be completed you could use either of the two (that’s the reason for the OR-operator in the logical operation).

If you now want to evaluate if a certain type of reaction occurs in a given organism it is sufficient to have one of the possible enzymes catalysing this reaction. So:

K01648 OR K15230 OR K15231