I believe you're linking to the wrong battery. Looking closely at the electronic speed controller PCB in the (cruddy, low res) pictures, those look like Traxxas connectors still attached to the ESC and you linked to a Tamiya connector battery. Whatever glob of plastic is on the ends of the ESC cables, I've done enough RC over the past decades to tell thats not tamiya connector, not even a heat damaged one, and enough ham radio stuff to tell its not a powerpole or remains thereof. The orientation of the connector does not look Deans connector like either. There really are not many popular RC battery connectors out there. One interesting point to note is the Tamiya connector battery is Amazon's 3rd best seller and although I haven't figured out which Tenergy battery w/ Traxxas connector this is, I'm sure its sales rank is way below 3rd.

You can trivially google for RC car traxxas connector and compare the pics to the pix of the ESC used.

Of course the overall "project" was probably kit bashing a ready to run full kit, not buying bits and pieces off amazon one at a time. Of course if you google for ready to run RC cars sold with traxxas connectors and tenergy batteries there really aren't that many possibilities. So that is interesting. If they find the remains of the RX that should probably narrow it down to like, one model of car or something. At which time things will likely get exciting for retailers of that ready to run model...