The wood is the fake kind, not actual wood, found in cheap furnture. The scratches were made by a cutter knife.
Depending on how deep the scratch is. Before more typing, why not just place a table cloth over the scratch since it is what you said? To "fix" finishing on wood furniture requires techniques, and costs on materials. Is it worth the fixing? looked like it's all the way across edges.
If the surface is real wood you can sand the marks out then refinish the surface. If fake wood you can rough the surface and overlay with a laminate. Trim edge with flush trim router bit.