You might also look at the alignment of your derailer. The picture may be distorted but it looks like the tail of the cage is slightly inboard. This could cause your problem.
Yes, you need that pulley at the bottom. Alternatively, you could add a cable stop on the seat tube using
this from Problem Solvers. You’d need a top pull derailer but the routing would be better especially since you seem to be missing the pulley.