It seems as though much of the discussion assumes a hedonistic theory of well-being (or at least uses a hedonistic theory as a synecdoche for theories of well-being taken as a whole?) But, as the authors themselves acknowledge, some theories of well-being are not purely hedonistic.
It is also a bit misleading to say that “many effective altruists are not utilitarians and care intrinsically about things besides welfare, such as rights, freedom, equality, personal virtue and more.” On some theories, these things are components of welfare.
The two main rivals of hedonism are desire theories and objective-list theories. According to desire theories only the satisfaction of desires or preferences matters for an individual’s wellbeing, as opposed to the individual’s conscious experiences. Objective list theories propose a list of items that constitute wellbeing. This list can include conscious experiences or preference-satisfaction, but it rarely stops there; other common items that ethicists might put on their objective list include art, knowledge, love, friendship and more.
It’s discussed a bit here: