While a man was walking, dressed in fine clothes and admiring himself, with his hair well-combed

The Prophet (may Allah's peace and blessings be upon him) recounts that a man was walking arrogantly, wearing fine clothes and his hair well-combed, and all of a sudden Allah caused the earth to swallow him, and so he fell and disappeared deep inside it, and he keeps sinking therein until the Day of Judgment. Because of his arrogance, self-conceit, and self-admiration, the earth swallowed him.

"He continues to sink therein” probably means that he is still alive in the real sense and will continue to be punished that way inside the earth. In other words, he gets tortured as living people do. Another possible meaning is that once he sunk into the earth, he died and yet he keeps sinking into it while being dead. Thus, this occurs to him in the Barzakh life, the interval between worldly life and the Hereafter, in a manner unknown to us. What matters is that this is his punishment .