Why am I not leveling up?

According to this page, with 400+ experience, I should be level 4 by now.

But as you can see in the following picture, I'm still level 2. Why is that happening?

According to this page from the guide you linked:

The hero starts the game near a different town, according to the virtue he/she chose. First thing to do is to get to Britain and to the nearby Britain Castle, the only place where a character can level-up.

Any party member can earn a level when he or she has the sufficient amount of experience points. Talk to the king, and he will raise the Companion's level by 1, the health points by 100, and the three attributes by a random number between 1 and 7.

So it sounds like you need to go to Lord British to cash in your earned experience.