Hi UnderMind and welcome.
after reading your story I feel there are 2 different issues here.
1. does your wife really have to play by the same rules you do;
2. did you both agree on the rules and did she now break them?
Issue #2 is something that needs negotiating between the two of you. Issue #1 is something that you need to figure out for yourself, if you can be at peace with that. I'm in a slightly similar situation - my husband is dating someone who has not told her other boyfriend about her relationship with my husband. It has taken me a LONG time to accept that this is ultimately his decision and not mine. But, we never agreed on a rule or boundary that said "we both cannot date people who are cheating". So while I am uncomfortable with it, and hope that things will change, for now I accept things as they are, and do not feel that he broke 'our' rule.
and FWIW, I don't consider not meeting the other partners(s) of someone I'm dating, unethical. (but I know that there are some very different opinions about this here on the forum). Every relationship is different and can come with its own set of rules. The most important thing right now seems to be that you listen to your wife and understand why she would be willing to start a relationship with this guy follwowing his rules, and that she listens to you and tries to understand why this is diffucult for you. The outcome could still be that she does something you are not completely happy with, but the big difference is that you would feel heard and respected. At least, that is what has worked for me in my situation.