You cannot "fix" it without replacing the floorboard, but you can patch it to look close.
That looks like IKEA's pressboard laminate - that's not wood you're seeing, that's paper. You can check their stock for some extra boards if there's one near by - sometimes they might have some extras in returns.
So - get yourself some dark stained wood filler and a 2" putty knife, and a small "wood stain marker" that matches the color more exactly. You can find all of these in among the paint aisles in any big box hardware store. You'll also want some 100 grit and 220 grit sandpaper.
Fill the hole with filler and smooth with the knife. Let it dry and sand smooth first with the 100 grit then the 220 grit.
Finally, stain the filler to match, and let dry.
When using Oxalic acid, which usually comes in a dry crystal form, mix it with hot water, as hot as you dare, reading the labels for mix ratios. I mix it a bit stronger than they say, but that is me, I do stuff like that. You are new to this I don't recommend you do that, stick to the directions.
While the mix is hot, pour it on the floor the same way the stuff that stained the floor did. Let it set as long as it takes to get into the same places as the fluid did that did the damage. According to the end grain discoloration, it was wet for a long while.
Keep it wet, keep the mix hot if you can, the hotter it is, the easier it works, the faster it will soak into the wood end grain. Do not let it dry out over the time while you are working with it, keep it wet.
If you went really overboard with the acid, I don't think you would ruin the flooring. Yes it will swell a bit, but it will dry back out. Any small gaps created by the flooring swell, will far less noticeable than the gray streaks the stain has.
The trick about keeping it wet is, when oxalic acid dries it forms at the least a white haze. Not dry=no haze. If it does haze add more acid, a simple fix. The important thing is the cleanup. Have a clean 5 gal. bucket of water, a scrub brush and plenty of towels. Use the brush with plenty of water, drying it up with the towels. Do this 3 or more times, 5 is not out of the question, cleaning MUST be thorough. I had done this on wood walls with a hose and brush with constant running water and still had haze here and there.
Let the floor dry out for a couple of weeks before trying to repair the finish.
Best Answer
A small amount of a good quality hardwood floor wax should hide those scratches. I mean like a paste type wax, something that is solid at room temperature.
Furniture polish would hide the scratches, but the oils would make the floor dangerously slippery. So a solid type wax prevents the oily problem. You may need to warm a small amount of the wax, so that it soaks in. But test it first on a 1" part of one scratch, to be sure this is the right path, as it could make the scratch darker. So test the repair on a small section before applying to the entire scratch.
A second option would be to apply the same finish to the scratch that is on the floor in the first place. To do that you may need to contact the flooring manufacturer, or if it was finished after it was laid, you will need to get that info from the contractor that finished it.