Was confused by that as well. Sounds like Liquid Democracy doesn't do well compared to the alternatives, which would certainly be an interesting result, but doesn't fit with what the rest of the abstract seems to be suggesting.
Perhaps that latter is because they are OK with representative democracy in principle, but want the capacity to revoke & reallocate their vote without waiting months or years for an election.
I found the study disappointingly shallow and conclusory by comparison to the usually excellent standards of the NBER, but it might be that the cost of surveying people limited the depth of their investigation.