Field Group Fields can't be empty since there's always at least 1 row so marking them required doesn't really do much right now. You need to mark the fields in the field group as required.

Does this need to be a field group? You mention selection. Wouldn't a single multi-checkbox or multi-select fieldtype that's marked required accomplish this?

You'll need custom validation rules to do that. The only thing I can think of is CB Code Field and its Code Validation functionality which lets you implement custom PHP based validation rules. The way it would work is when validating Field A you'd write the code to check if Field A OR Field B has a value and if it does then the field is valid. Example as follows.

Field A
Code Validation: Enable
Code (PHP):Ajax Validation: Enable
Additional Fields: FIELD_B_HERE

Replace FIELD_B_HERE with the name of whatever the second field is. You'd then select that same field in "Additional Fields" parameter for the client side validation behavior. Now just add more OR PHP cases and select additional fields as needed to add more fields to the validation check.

Now you'd edit Field B and do similar as follows.

Field B
Code Validation: Enable
Code (PHP):Ajax Validation: Enable
Additional Fields: FIELD_A_HERE

This should allow the fields and form to validate if Field A or Field B has a value.