is this intentional (the extra line on the blocks side)?

Ah no this is a rendering bug.

There are a couple of issues it causes

1. No selection box at all, usually the normal state
2. F3 will enable it again, but only until I change to another hotbar slot.
3. Diagonal line. Only happens when I open the chat input, otherwise it appears never.

If it is using GL_LINES, would not even be surprised, if behaves differently with another graphic cards model/driver.

This is most likely caused by the sky renderer i'd wager. I had the same issue with custom TESR code and will look into it here.