In the Sunraybe guide, I see that there are national bonuses (for example, the ability to move through 3 provinces for Pythium). Yet, they are not mentioned in the demo; does this mean that those bonuses no longer apply in Dominions II?
In many cases (such as the one you cited for Pythium), no. The national bonuses tend to be things like the healing available to the Arcosephalean forces via their Priestesses and the "auto-conjured" units that appear for nations such as Carrion Woods Pangaea.