Unlike some other languages, Latin for example, "or" in English has both what logicians call an "inclusive" meaning and an "exclusive" meaning. To clarify which meaning is intended requires additional words. Here what is intended is that those being excluded are only those with a conflict of interest. The "otherwise" clarifies that there is one general reason for being excluded rather than two although there are several ways that reason can arise.
If we were to say that we exclude those who work at the same institution or those with a significant conflict of interest, it would be possible to construe that as saying that working at the same institution is a reason for exclusion that has nothing to do with conflict of interest. That of course is not the intended meaning, and not many would interpret it that way. But experience has shown that some will misinterpret things unless they are totally unambiguous. It is in fact a favorite device of lawyers and politicians.
Saying we exclude those who work at the same institution or otherwise have a conflict of interest is not redundant; it avoids ambiguity. I must admit that if I were writing this, I would add further words because I do not like to accuse people of ignoring conflicts of interest. In what seems to be a relatively formal document, I would write "or otherwise may appear to have a significant conflict of interest."
VERY LONG EDIT:
As a result of the comments from the OP, I realize that my answer and comments relate to very extensive experience with conflicts of interest as they are addressed in the U.S. and with writing certain kinds of documents. This experience provides a context that undoubtedly informs my answer and comments, but is probably obscure to the fortunate.
First, there is a profound misunderstanding about conflicts of interest. Having a conflict of interest is neither a moral nor legal fault. If you are head over heels in love with your spouse, that is a conflict of interest: you cannot be impartial with respect to someone with whom you are wildly in love. This does not mean that people in love are criminals or moral outcasts.
A conflict of interest creates a potential problem only in those circumstances in which the person with the conflict is supposed to be impartial but will find it difficult or impossible to be impartial. That, however, is only a potential problem; it becomes an actual problem only if it is not addressed in an appropriate way. Here is how I wrote a policy on how to address such situations: "An officer or director who faces a situation in which a conflict of interest on a matter is likely to prevent or appear to prevent impartiality with respect to that matter must disclose fully and publicly the nature of the conflict, must not participate in any discussion on the matter, and must abstain from voting on anything regarding the matter, and furthermore may ask to be excused from or may be required to absent himself or herself from any meeting where the matter is being considered."
Note that the conflict is primarily the concern of the party with the conflict, and it is to be addressed by behavior, first by full disclosure and second by complete absention. Note as well that the language specifying that behavior is intended to be painstakingly clear.
There is, however, a completely different perspective, namely that of avoiding even the appearance of decisions not having been made impartially. This has to do with reputation rather than morality. This is often called avoiding the appearance of conflicts of interest. There is no implication that something wrong has been done in fact; it is to avoid the consequences of having wrongly appeared to have done something wrong.
Now let's get back to the specific case at hand. The editor cannot possibly be held responsible for knowing about all potential conflicts of interest between an author and all potential reviewers. The editor is unlikely to know that A and B started sleeping together three months ago. As I said, the person primarily responsible for addressing a conflict of interest is the person with the conflict rather than others. But people with conflicts do not always behave as they should. And if a review is found not to be impartial after publication, that is very likely in practice to reflect badly on the editor and publisher.
So the editor wants to avoid the embarrassment of having a reviewer fail to be impartial. But the editor has limited knowledge to prevent this. So, and I now speak as someone who has had to deal with such matters for decades, the editor makes a decision based on limited knowledge: colleagues at the same institution shall not be reviewers whether or not the editor has any knowledge or even a suspicion that a conflict of interest may exist, but the editor will exclude anyone else only when the editor has reasonable suspicions.
So to try to clarify any confusion i may have caused.
I do believe that the original document was badly written in one respect, but it is not because of "otherwise." Yes, the editor wants to avoid reviews tainted by a conflict of interest or bias regardless of the source. The OP is correct that "otherwise" is extraneous to that concern. But the editor wants in addition to avoid being wrongly accused of having ignored potential sources of bias or conflicts of interest and to avoid implying that anyone not selected did wrong. The editor has limited information to achieve any of those ends, let alone all three simultaneously. Therefore the editor excludes one disclosed class, colleagues at the same institution, without any negative information and therefore without implying anything negative against them. The editor excludes another but undisclosed class with some modicum of negative evidence. The distinction then is real. Disclosed exclusion without any evidence and therefore no suspicion on the one hand, and, on the other hand, undisclosed exclusion with evidence and therefore suspicion. That is the distinction that "otherwise" alludes to.
Is "otherwise" the clearest way to make that distinction clear? It would certainly be clearer if the purpose, which, as the OP has recognized, is the same in both cases, were better described because then it would be clearer why the distinction is being made. We are not just trying to prevent actual bias or a conflict of interest when we have evidence of it; we are trying in addition to protect ourselves from being attacked as careless or naive when we do not have evidence or from being attacked as accusing people without evidence. So I do not think the "otherwise" is at all superfluous. It points out an important distinction.
The question to me is whether "otherwise" is too subtle. Certainly, the OP did not see any need for it. It may well be too subtle if, as I believe, what is meant is
In order to minimize even the appearance of bias or conflict of interest, the editor does not select a reviewer from the same institution as the author whether or not the editor has any actual knowledge of potential bias or conflict. Nor, obviously, does the editor select any other reviewer who, in the editor's belief, may have bias or a conflict of interest.
Notice that no one, disclosed or undisclosed, is accused of acting improperly. Nor is any claim made that bias or conflicts of interest can be totally prevented. Instead all that is disclosed is an aim and a method. I think the clarification of purpose coupled with the "nor" is better than the "otherwise," but then I have been writing this kind of finicky stuff for at least forty years.