I don't think it says that.
As far as I can see from the Amazon preview, it says
mögen […] vt, vi to like
not "would like".
It then gives several examples, some of which use conditional forms such as ich möchte… or möchtest du etwas essen? which it translates with the conditional form of "like", i.e. with "would like".
But Duo's sentence does not use the conditional form of the verb wir möchten; it uses the indicative wir mögen. So the translation is not conditional "we would like" but indicative "we like".
Or which part of the entry are you referring to when you say that "CGCD5 states WOULD like is correct pg.229"?