First, the title "Artificial Intelligence Cracks 4,000-Year-Old Mystery" is a catchy title but a bit of an exaggeration. The work employed 1st-order Markov models (estimated using Kneser-Ney smoothing) to compute conditional entropy. Markov models can only be regarded as a first step towards the application of more powerful graphical models and grammar induction techniques in AI to the Indus script problem.

"The underlying grammatical structure seems similar to what’s found in many languages"
Should be:
"The underlying grammatical structure, as compared using conditional entropy, seems similar to what’s found in many languages"

"Even though we can’t read it, we can look at the patterns and get the underlying grammatical structure."
Should be:
"Even though we can’t read it, we can look at the patterns in sign sequences to try to get at the underlying grammatical structure."

When they seeded the program with fragments of Indus script, it returned with grammatical rules based on patterns of symbol arrangement.
Note: The Markov model encodes patterns in terms of transition probabilities from one symbol to the next, not grammatical rules.

"It's only recently that archaeologists have started to apply computational approaches in a rigid manner"
I am not sure this sentence even makes sense!
Should be:
"It's only recently that scientists, in collaboration with archaeologists, have started to apply computational approaches to the script problem in a rigorous manner"