It looks to me that the only difference from the typical scheme is that the state is shown as separate nodes; you could instead show it as a single node with two components A = (a_1, a_2) and it would look like a regular Hidden Markov Model with one hidden node.
I’m not sure how common this is in HMMs, but in the general state-space formulation there would normally be vector-valued states, which could also take continuous values instead of discrete (I came across a model that I thought of formulating as an HMM but couldn’t really figure out how and I ended up concluding that it was worth thinking of it as a general state-space model). The advantage of this is that it is general.
The advantage of the former is you can compute a closed-form likelihood and inference should be a lot easier. I’m guessing you can write down the (Markovian) update step and work out the recursion to get: P(X) = \sum_A P(X|A) P(A), you will just have more state possibilities to sum over. I’d be curious to see if this works out if you carry it through.