Look at the table. The top line gives armor classes from 2 to 10. The attack matrices (in the DMG) run from AC 10 to -10. There's a reason for that. The table you reference began its life in the Chainmail rules, where there were no "+1" or "+2" magical armors, and the numbers referred to types of armor, not to numeric ratings of protection.
In 0e's Monsters and Treasure (2nd book of the 3LBBs), the description of magic armor begins thus:
Note that this is using the Chainmail combat system, not the "alternate" combat system which we all know and love (because the alternate system officially became the default system in 1E, but was unofficially the default for anyone who came to the game without playing Chainmail first). Translated, this means that the original system did not apply the bonus for magic to the armor class, but rather to the attack roll (as a penalty). In the earliest games, armor class was not meant to be a numeric value of "protection" but to describe the type of armor in briefest terms. However, it did not escape DMs or players at the time that you absolutely could add the bonus to the AC as if it were that sort of protection value; those with less history in the game may have thought that's how it was supposed to work. Those were also the people who did not understand (as I did not, back then) that it was armor type and not value that was being used in that confusing table.Armor proper subtracts its bonus from the hit dice of the opponents of its wearer. If the shield's bonus is greater than that of the armor there is a one-third chance that the blow will be caught by the shield, thus giving the additional subtraction.
Greyhawk actually introduced the table more or less as you've shown it from the PHB, but since that game started at AC 9 and still had AC 7 leather, AC 5 chainmail, and AC 3 platemail, there were some changes between them. 2E kept the concept but dinked with the table somewhat; most significantly, it changed the armor types to names rather than numbers, to avoid exactly the confusion you're expressing above.