It was a simple search. You could have easily searched for glucose oxidase in KEGG, and you would have got this reaction.
In fact if you had clicked the link for glucunolactone's _compound_ page, you would have got a list of many different reactions that convert glucose to glucunolactone.
You can even click the arrow which opens the _KEGG-ORTHOLOGY_ page. You can find a field called _RN_ in the section called "Other DBs". The links corresponding to this field would give you the exact reactions, that the pathway uses.