We have multiple examples in the OT of a woman executed or almost executed for the crime of adultery. Her lover was also liable to execution.
Would you care to provide an example of a man considered guilty of adultery not because he had sex with a woman married to someone else, but because he had sex with a woman other than his wife?
In a polygamous society male adultery in this sense has no meaning. Even a man convicted of raping a virgin was only sentenced to pay a fine to her father and be married to the rapee without possibility of divorce. No mention of his execution if he happened to already be married. It was just not relevant.
You are correct that male adulterers are to be put to death, as they are today in Saudi. But the crime is defined as sex with a married woman. Not sex by a married man with someone other than his wife.
Definition of adultery in the OT: “22 If a man is found sleeping with another man’s wife, both the man who slept with her and the woman must die. You must purge the evil from Israel.”
You will notice the absence of mention of a woman sleeping with another woman’s husband.