"This flow of electrons into into the lead dioxide (PbO2) electrode, gives it a positive electrical charge."
and "The flow of electrons out of the lead electrode gives it a negative electrical charge."
I am no expert, as I am reading this to learn, but these descriptions do not make sense to me and are possibly an error. When electrons are gained, isn't there a negative charge? and a positive charge when they are lost?

 

That section describes the assignment of polarity to the terminals of a battery. The negative terminal sources electrons and the positive terminal sinks electrons by convention.

The diagram below the statements shows that within the battery during discharge, electrons flow from the positive electrode to the negative electrode.

Perhaps it could be better written, but in context of the paragraph and illustration, it is correct.

John