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Oddly, the test suite skips getoutput and getstatusoutput on windows with the comment that the source says it is relevant only for posix, but the documentation does not have 'availability: unix' tags. (It is also odd that getoutput isn't documented, but that's a different issue.)
Your workaround can't be used as a fix, since the semantics of {}s in the shell are different from those of ()s.
It's not clear to me what the point of the {}s is, but I have a fear that eliminating them would introduce subtle changes in the behavior of getoutput calls. Perhaps not, though.
It looks like this issue amounts to an RFE for support of getoutput/getstatusoutput on Windows, though the fact that it is not documented as unix-only may make it a bug instead :)
The appropriate fix is probably to conditionalize the code based on platform. A complete patch will require unit test changes and documentation changes (since the docs currently mention the braces).
All of that said, it also appears that the new check_output should be preferred to either getoutput or getstatusoutput. Perhaps those functions could be re-implemented in terms of check_output.