If you don't want to list all your columns in CTE, another way to do this would be to use outer apply:
select
s.logcount, s.logUserID, s.maxlogtm,
a.daysdiff
from statslogsummary as s
outer apply (select datediff(day, s.maxlogtm, getdate()) as daysdiff) as a
where a.daysdiff > 120