Return values from Left Table Only Once
This could be solved with an EXISTS subquery 

select
    rs.ID,
    rs.event1,
    [Exists] =
        case when exists
                ( select *
                  from #bigponyhorses as bph
                  where rs.uuid = bph.uuid
                    and bph.empid = @empid
                ) 
            then 'Yes' else 'No'
        end
from 
    #robschneider as rs ;


or with OUTER APPLY operator:

select
    rs.ID,
    rs.event1,
    [Exists] = coalesce(b.result, 'No') 
from 
    #robschneider as rs
  outer apply 
    ( select top (1) result = 'Yes'
      from #bigponyhorses as bph
      where rs.uuid = bph.uuid
        and bph.empid = @empid
    ) as b ;


The TOP 1 is needed when using OUTER APPLY to make sure you get in the result one row for each #robschneider, even if there are 2 or more matching rows in the #bigponyhorses table. If there is a UNIQUE constraint on #bigponyhorses (uuid, empid), then it's not needed.