Is what is meant by this statement "he who raises his gaze intentionally while supplicating," and is the unintentional excused, and is what is meant by "raising the gaze" not "looking," and is raising the head without raising the gaze considered normal?

It is disliked for a worshiper to raise his gaze to the sky during prayer, due to the Prophet's (peace be upon him) prohibition of that and his severe warning to anyone who does so. This is because devotion is required, and the worshiper stands before Allah, supplicating Him, so he should be humble, lowering his head towards the place of prostration.

If the worshiper raises his gaze inadvertently, there is no dislike.

Raising the head during prayer necessitates raising the gaze, and the dislike remains even if he closes his eyes, because the reason for which raising the gaze was prohibited is present, which is not looking at the place of prostration.

An exception to this is raising the head out of necessity, such as burping, in which case there is no dislike.