In a previous life

I was in the furniture business and developed an ability to refinish wood furniture as a result.
So, assuming that corner is real wood, and not pressed wood, or some other product, and depending on how much of a perfectionist I want to be, the only way to get that back to looking real nice is to completely sand it off and stain it. Then I'd let it dry for several days or more, and put some poly over it, or maybe a lacquer. I'd probably tape it all off real nice after staining, then I'd spray it, most likely with lacquer.
Now, if I were in a hurry, and the finish on there isn't flaking and chipping off all over, I'd maybe just sand it a wee bit with some 220, or finer grit sandpaper, or maybe just scjuff it with some 0000 steel wool, and then just get a rag, fold it up, stick the corner of that rag in some walnut stain, and go over it with that.
And for what it's worth, I have several of the stain/markers in my desk drawer right here at home. I use 'em all over the place, including our hardwood floor

They're great for touchin' up stuff, but with a larger area, if I don't want to do a complete sand off of the item, I'll just get that rag, and some stain, and after prepping the piece a wee bit, just go over the whole thing with stain.