It's more a case of speaking different "emotional languages" than a strict deficit.
Indeed that may be a cause of impaired theory of mind in many autistic individuals. It would depend on what the narrow tunnel of attention is focused on. A narrow (and deep - I failed to say that earlier) tunnel of attention focused on another mind, say an autistic psychotherapist, or better an autistic psychotherapist focused on autism, may have a greatly heightened theory of mind.
Perhaps tangential, but consider Temple Grandin's exemplary work designing animal handling facilities that work much better largely due to treating the animals better - often with changes or accommodations to things that nobody realized caused the animals stress and anxiety, often by putting herself in their place.
The fundamental mechanisms that make an autistic brain different than the statistical average brain are not yet fully understood, I know. But this study we are talking about is not about the fundamental mechanisms.
I just got out of a relationship with a French woman because of our differences in cultural norms, she also had an accent and we used idioms and expressions that neither of us were super keen on. We both lacked a robust theory of mind of each other. I had an impaired ability to ascribe mental states to her. And I find it very unlikely that I will ever become fluent in French. I currently and probably always will lack that capacity.
I also have an impaired ability to ascribe mental states to Donald Trump, and my cat. But most people would consider me allistic. Because I have mental processes that allow me to ascribe the mental states of other statistically normal people. Within the context of statistically average people, of my own culture, I have a robust-enough theory of mind. ToM is not binary, but a degree, and context dependent.
"Mental conditions" are classified mostly because they are disadvantageous or uncomfortable to some group of people. They can only be classified in relation to normal social behavior at some degree of deviation. Shouldn't it be implied that allistic people also have an impaired theory of mind of autistic people.
Taking Wikipedia's definition of ToM, it specifically mentions "capacity". So when you mention that autism may be a "narrow tunnel of attention", this feels very consistent with the definition of ToM. If my attention is extremely narrow, then I will have an impaired ability to understand other people by ascribing mental states to them.