Electrons are removed along with the hydrogen ions in the above case. It is not the same thing as when you abstract a proton from an organic molecule in a simple acid and base reaction, and this might be where the confusion is arising. In the acid base case, when the proton is removed as H+, the electrons that were bound to the hydrogen are left behind on the organic molecule afterwards leaving the organic molecule with a -1 charge.
In the present case, after removing 2H+ protons the organic molecule is not left with a - 2 charge afterwards; it is neutral. The only way this can happen is if the molecule lost 2 electrons along with the protons (and loss of electrons from a molecule is an oxidation). A common way you may see this type of oxidation written is to see protons leave as 2H+ + 2e- in biochemistry diagrams.
Later on you will learn that these biochemical reactions don't occur as easily as simple proton exchange reactions in general acid base chemistry. The body has special molecules such as NAD+ that can carry a proton and two electrons away at the same time (as NADH).