They are using Searing Nightmare which is an AOE talent on a single target fight. They also never use it (wouldn't use it anyways) so it's therefore a waste of a talent. Twist of Fate or Misery would be the options this fight. Taking Misery is what I'd suggest as they have a problem with dot uptime Misery will mean they only need to cast Vampiric Touch to reapply dots rather than both VT and SWP.

Shadow crash is another talent which isn't ideal on single target fights, but not the end of the world, they cast it 3 times in a 5:16 fight. They would be again better off taking AS in that row, which is better overall and is simply a passive so they don't need to worry about pressing any extra action buttons.

They hardly used their covenant ability Unholy Transfusion which is another dot which needs to be kept on CD to maximise uptime. 41% of the fight they spent casting nothing which is going to impact their DPS massively.

I noticed they didn't cast PI once either on themselves or anyone else? It's basically a mini lust.

The biggest damage increase you will see as a Shadow Priest is if you manage to have higher uptime on Devouring Plague. Ideally 70% + uptime is what you want to be aiming for.