I must admit to only having had a quick glance at this, but couldn't you do something like this instead?

SELECT EmployeeId, MIN(LoginTime) AS LoginTime, MAX(LogOutTime) AS LogOutTime

FROM (SELECT DENSE_RANK() OVER(PARTITION BY base.EmployeeId ORDER BY base.LoginTime),

base.EmployeeId, base.LoginTime, overLap.LogOutTime

FROM Overlapping base

INNER JOIN Overlapping overLap ON base.EmployeeId = overLap.EmployeeId

WHERE (overLap.LoginTime > Base.LoginTime AND overLap.LoginTime < base.LogOutTime)

OR (overLap.LoginTime = base.LoginTime AND overLap.LogOutTime > base.LogOutTime)

AND base.DKey <> overLap.DKey

)a(pos,EmployeeId,LoginTime,LogOutTime)

GROUP BY pos, EmployeeId;

Don't know whether or not it'd be any faster. . . could probably do with a performance check but I haven't really got the time to knock up a million row sample test to check.