I've mentioned before that the Hartnell era was one in which the BBC really hadn't started thinking of television as a medium in its own right; in their mind, they were producing live theater with an audience they couldn't quite see. This theatrical inspiration can be seen strongly in 'The Edge of Destruction' and 'The Brink of Disaster', which plays like an effort from Sartre or Pirandello, and as the plot of this story kicks into high gear, it can also be seen very strongly in the Shakespearean convolutions of 'The Warriors of Death'.
The obvious parallel here is with Tloloxl, played by John Ringham like an extremely experimental version of 'Richard III'. Actually, no--that's what everyone says, because they notice his gait and his slightly nasal speech, which is how King Richard III is traditionally played, but he's really doing Iago. The director does a wonderful job of constantly putting him just a little bit upstage of every single character he speaks to...he's constantly whispering in everyone's ears, insinuating and promising and plotting. Constantly plotting, really; when he promised at the end of 'The Temple of Evil' that he was going to destroy Barbara, he didn't muck about. He forces Autloc to put Barbara through a series of grueling tests on religious doctrine, he frames the Doctor for violations of temple protocol, and he sets Ian up for a duel to the death in a scene with the Perfect Victim that is an absolutely letter-perfect manipulation. We are now officially light-years from Tegana and his overt mustache-twirling, here. Tloloxl is subtle, conniving, and in perfect command of the situation.
And of course, he's helped by the Doctor. The subplot where the Doctor's efforts to find a way back to the TARDIS inadvertently help Ian's nemesis Ixta is exactly the kind of thing Shakespeare loved. Mistaken identity, chance and coincidence conspiring to bring about tragedy, and of course a good old-fashioned Poisoned MacGuffin that owes more to the laws of drama than the laws of nature. (Oh, and a contrivance that furthers the plot in an ironic fashion--the Doctor's shout to Ian is exactly what causes him to drop his guard long enough for Ixta to scratch him.)
If this was a traditional Shakespearean play, though, the duel between Ian and Ixta would be the climax. Instead, we're at only the halfway point, and Ian's story serves only to advance Barbara's main plot. This is also Doctor Who when it's at its most ensemble-oriented, and Barbara is allowed to be the protagonist for a story in a way that Martha or Clara never are. As such, Ian is the peril monkey, the Doctor is held prisoner and it's Barbara who has to save the day. Which is frankly just awesome, full stop.