As far as I can tell there are two other explanations, one easy and simple and one fairly complex:
1. The Terminator in the first movie wasn't a T-800 unit. Not sure, but I do believe that this unit and the similar unit in the sequel were both 'mere' T-100 units. If my assumption is correct (and it *is* and assumption - I'm by no means certain that I'm correct), then it would seem that the T-800 units are an 'upgrade' of the original T-100 units.
2. The facts and speculations about the 'old' terminators in the first two movies no longer apply because the timeline was altered when they managed to stop Judgment Day in the second movie. Therefore the future that the subsequent terminators come from is a new or alternate future. As we learn in the new film (without spoiling anything), the future was indeed changed or at least postponed due to the events of the second movie, and so technology would likely have advanced further by the time the terminator units came into production.
(Damn, I *hate* changes to the timeline - this is starting to sound like a bad episode of VOY or ENT... oops, I'm still typing!)
"We think we've come so far... Torture of heretics, burning of witches - it's all ancient history. Then, before you can blink an eye, suddenly it threatens to start all over again..."
- Captain Picard, "The Drumhead" (TNG).