I think the split is just in terms of scope. You split product vs. platform because there are different scopes. Same as you may split teams focusing on "the messaging feature" and "the image manipulation feature". That is just scope of work.
However, IMO, regardless of that scope, every engineering team should take a product-oriented mentality. They are producing something that someone else will use. And they need to understand needs, requirements, manage users, etc. Of course who the customer is will vary many aspects, but the core of the matter is the same: every engineering team needs to do adult product management.