The other answers have addressed the matter of correctness and parsing: the phrase is 'suffer more', and that's compared with 'others'. This answer addresses the issue of why the phrasing works, given that the phrasing 'suffer more than others' is more familiar to you.
Choice of phrase often depends on context. Here, the context is a dictionary entry for the phrase "come off worse". The word worse is a very important component of this phrase. Since it is fundamentally a comparison, the example highlights the comparative aspect ("compared with").
The phrase "suffer more than others" highlights the suffering of the unnamed person. Changing than to compared with shifts the stress to the comparison.
- Peter suffers more than John.
- Peter suffers more(,) compared with (or to) John.
In English, stress is sometimes expressed by using 'less common' or 'more unusual' phrasing - the phrasing is said to be marked.
In linguistics and social sciences, markedness is the state of standing out as unusual or divergent in comparison to a more common or regular form. In a marked–unmarked relation, one term of an opposition is the broader, dominant one. The dominant default or minimum-effort form is known as unmarked; the other, secondary one is marked. In other words, markedness involves the characterization of a "normal" linguistic unit against one or more of its possible "irregular" forms.
It's arguable that 'compared with' is the marked form, compared with 'than' in that context. Alternatively, one might argue that the stress was created by using the longer phrase, or simply that the comparison was made explicit by using the word "compared". Whichever the case, the focus is on the comparison.
Finally, a note about the parsing. Having read the quote several times, I think the natural parsing is:
- [to lose a (fight, competition, etc.)] or [(suffer more) compared with others].
In particular, "compared with others" only applies to "suffer more", not to losing the fight and so on.