Shakespeare is one of those historical people that seems so obvious for Doctor Who to visit. Which is probably why the show avoided it until the Tenth Doctor and Martha. Yet this one does a much better job because it plays up the tropes of Shakespeare so much more, and is more about a performance than the writer, and only plays that card after it's well and truly built up.
The main bad guy, General Mariah Learman, a woman who thinks so highly of Shakespeare she's now decided that the rest of Britain doesn't respect his work, so she's creating a time machine to watch the first ever performance to watch Julius Caesar and record it. Oh, and kill Shakespeare with the help of the Daleks. She's so obsessed that even her speech patterns are like his writing. Which the Daleks join in on, which is really weird.
Learman's speech pattern does two things though. First it shows just how unhinged Learman is, right from her first appearance you can tell something isn't quite right. Secondly it really makes the whole thing a lot more Shakespearean.
Then there's the character Kitchen Boy. A character that sounds like it's voiced by a woman. Women voicing young boys in audio work is nothing new. One of the most famous animated boys ever, Bart Simpson, is voiced by a woman. It means that you don't have to worry about silly things like puberty, or ability to act. Then they reveal that the Kitchen Boy is actually a young Shakespeare, taken out of time for safe keeping. It's a nice reversal of the old tradition of young boys playing women, and also the trope of the last minute reveal of a background character.
But again, we're in Dalek Empire 0 part 4, and I still couldn't see the connection. Then suddenly Big Finish smack you with it. In fact it's a very nice bit of timey-wimey to pull the four parts together. It's proper time travel battle, and more importantly for the Doctor, it's the reverse of what he did in 'Seasons of Fear'. These four events might be well spaced for the Doctor, but for the Daleks it's all part of one scheme.
They got information from the Library of Kar-Charrat, they got some more during their invasion of Gallifrey. That alternate timeline they accidentally created is the reason there's an entire fleet stuck in a temporal hole, and the final bit of random time travel even connects back to 'Seasons of Fear' and explains where that random Dalek came from you could hear right at the end.
I can't help but feel it's a retro-active tie-in though, the first three might have been some of the earliest Big Finish adventures. Likely so they could get the chance to play with the Daleks if they only briefly had the license. But Part 4 was a full two years later. Not that that's an issue. In fact it's quite the opposite. For Big Finish to come along and tie it all together in a neat bow is some fantastic writing. I've long understood the position that Big Finish not only kept Doctor Who alive, but it flourished under them. I'm coming to appreciate why that is. The Time of Daleks is a prime example of exactly how.