Deadlifts will hit most of the posterior chain, but to really grow thickness in the upper and mid back you'd need to add in heavy rows and/or pull-ups as OP mentioned.
Might as well chime in with the basic back-of-a-napkin strength program -> One movement for: (1) vertical push, (2) vertical pull, (3) horizontal push, (4) horizontal pull, (5) glutes/"back of your legs", (6) quadriceps/"front of your legs".
To beat the dead horse, deadlifts definitely involve pulling but it's primarily a glutes exercise. Adding in dedicated pulls like pullups and rows will give you a lot of bang for your buck.
Well, if we're all chiming in: another requirement is a caloric surplus. Beginner gains are a real thing, but at a certain point (say 8-10 weeks) a caloric surplus will be required to continue seeing changes in strength and muscle mass. And that reminds me, the weights also need to get incrementally heavier.
As an armchair gymmer, this routine lacks pull exercises for back musculature. Add row pulls or pullups!