Laminate floor sliding out of place
What happened is that you broke off the MDF tab that was holding that plank in place. That's why it slides freely now; nothing's mechanically holding it in place anymore. Since the core is MDF, any kind of wood glue should be totally fine to fuse them together, and once glued, those two planks will probably be more strongly held to one another than the other ones that are only mechanically fastened. Once you apply the glue, tape the planks together with masking tape or blue painter's tape to prevent the glue from expanding and pushing them apart.

If you really wanna make sure it never comes loose again, you can get some of the wood wood glue that's specifically made for this use: Titebond!