I mean it uses a much logic as a Markov chain typically does which is use patterns in inputs to make an output. It will generate melodies, harmonies, rhythms, ect that are not necessarily music theory concepts. If you fed a Markov chain any book it will seem to make logical sentences, but it will not always be that way and the chain doesn't actually understand the langue it just looks for patterns and the result may or may not make sense. This same idea goes for music as it will There statement about how it's done is:
The Flow Machines project takes a computer science perspective on
style: how can a machine understand style and turn it into a
computational object? An object that users can manipulate to create
new objects with their own constraints. Technically we develop new
technologies based on Markov models. Markov processes are well-known
tools used to model statistical properties of temporal sequences.
In general the Markov chain alone is pretty weak in making music and in fact you will need at least a second order Markov chain to make anything make sense from a harmony perspective since tonal music's harmony goes somewhere. The key also is pretty important as the notes used in the melody and harmony will not be equally weighted for example how a C major chord is used in C major vs F major is different. In fact, the example video shows this weakness pretty well as the chords used and the melody kind of make sense, but it isn't very natural and has the meandering effect a low order Markov chain as the melody doesn't find a good point of rest.
They mention grouping styles which will help minimize these issues as mentioned in your second link:
We are currently investigating style and creativity under several
perspectives: Technically we have made substantial progress in
developing efficient Markov Constraints algorithms that can apply many
types of constraints to arbitrary Markov models. Conceptually we are
starting to build authoring tools in musical composition and text
writing that enable people to generate content by manipulating the
style of an existing author, possibly themselves.
Again this is not theory, but just using inputs to make an output. The chain won't understand any of the actual music theory concepts nor will it always do things that make musical sense. There's even a big red flag further down that page:
If you don’t like the proposed sequence the system will suggest
another one, and so on until you are satisfied with the result.
Which is just a way of saying "take another chance and you may like what you hear". While using a Markov chain is better than just randomly picking notes, duration, ect, it's still a long way from being aware of what it making or any of the theory behind it.
I'm not going to speculate on the exact mechanics and without looking under the hood I won't know for sure, but based on everything and what they are describing there is little to no actual music theory behind it. The only thing that is kind of theoretical is grouping the pieces by "style" before making the chains, but that's not really music theory as it is just grouping pieces that whoever made the groups thought they were similar.