How to Fix Dried Play-Doh Damage to Floor

My SIL scratched her laminate floors. She replaced the plank like you are talking about. As long as they are the snap together kind and not the adhesive, it should work. It's a pain though. You have to start on one side and pull up the planks starting at the wall until you get to the damaged piece. Since they snap together you'll have to take out a rather large section to remove and replace the piece. When my mother scratched her floor, she found a scratch repair kit that camouflaged the damage her chair caused. It's not very noticeable, not sure if it would be missed on a walk through or not though. It might be worth trying one of those kits first.

I would have a professional do it, not yourself.
Because you are renters.

Laminate flooring is interlocking. Thus, you cannot just pull out that one single plank. You have to also pull out all the surrounding side planks to it... like a domino effect. THEN lay it all back together. Properly. And, depending on how it was installed, what if they glued it down? Unless it is floating?
And, the new replacement plank... may or may not, 'match' exactly, with the rest of the existing flooring. Sometimes, the coloration of the floor can overtime, darken up or lighten up, due to sun etc. If this is a wood laminate flooring. Not synthetic wood.

Or maybe you can try wood putty.
Try going to your local hardware store, and ask them about fixing wood gouges.

You should take a plank to a local flooring place and ask them the questions.

When we moved into our house in CA the movers deeply scratched our wood floor. When they send a flooring guy to replace he said it was real wood, but with a thick laminate style coating onto it. His recommendation was not to sand it down because of the coloring (or something). He said since we found (after we moved in) additional flooring planks, was to actually leave them by the area that was damaged for a couple of months because of fading and then have them installed. This way the wood would match better. We never did it, I ended up throwing an area rug over it!

I missed that the floor is a laminate. My advice was for wood. Sorry.

Being a landlord myself, I would much prefer my tenant call me about it. They may have done it themselves and be able to tell you how to fix it, or let you know who to contact. It'd be much worse if you ruined the whole area, trying to do the right thing.

They might be especially forgiving if you go above and beyond with making the rest of the house look ready to rent out.

I would ask someone at, e.g., Home Depot.