Actually there is divorce in that world since they mentioned it. They probably mean that the specific vow they made is a lifelong binding contract and doesn't have a way to get a divorce
I think it's a novel reason for the other LI to be compulsively like their game selves, I rather like it and hope it'll go in an interesting direction~
Ty for the translation and sending well wishes to the translator~
And a world without divorce is scary because abuses of power and unconditional union obv.