we should wonder what these terms could signify that does not entail a preference for the Good Life?

Are "what" and "that (subclause)" the double objects in the sentence (clause) "we should wonder what these terms could signify that does not entail a preference for the Good Life over the Bad Life"?

By that I've meant:
Does " what these terms could signify that does not entail a preference for the Good Life over the Bad Life" mean "what these terms could signify when talking about that does not entail a preference for the Good Life over the Bad Life"?

Context:

There are actually people who claim to be unimpressed by the difference between the Bad Life and the Good Life. I have even met people who will go so far as to deny that any difference exists. While they will acknowledge that we habitually speak and act as if there were a continuum of experience that can be described by words like "misery,""terror," "agony," "madness," on one end and "well-being," "happiness," "peace," "bliss," etc., on the other, when the conversation turns to philosophical and scientific matters, such people will say learned things like, "but, of course, that is just how we play
our particular language game. It doesn't mean there is a difference in reality." One hopes that these people take life's difficulties in stride. They also use words like "love" an "happiness," from time to time, but we should wonder what these terms could signify that does not entail a preference for the Good Life over the Bad Life. Anyone who claims to see no difference between these two states of being (and their concomitant worlds),
should be just as likely to consign himself and those he !°loves!± to one or the other a
random and call the result !°happiness.!±