Try running the
select count(MT.MovieID)
from MovType MT inner join Category C
on MT.[type] = C.[Type]
group by C.[Type])
part of your statement sparately. You will probably find it is returning mulltiple records and hence the set MovieNumber = statement will fail with your error as it can not update it to multiple values.
Also you will need a where clause at the end so only the appropiate record is updated.
Try
update Category
set MovieNumbers = numb
from
(select count(MovieID) as Numb, Type from MovType group by Type) x
where x.type = category.type