The adverb form: to do something — usually to stare, gaze or look — with your eyes open and your mind absent. 'She stared unseeingly at the screen' means the screen was in front of her and she took in none of it. It attaches to verbs of looking almost exclusively; you would not normally say someone walked or ate unseeingly, though a novelist might. This is even more bookish than unseeing itself, and rather rare — writers often prefer the shorter 'stared unseeing at the wall', which does the same job. Meet it in fiction, recognise it, and do not feel you must use it.

茫然地、視而不見地（多修飾 stare、gaze 等「看」的動詞）。書面語，比 unseeing 更少見。