I see two critical problems:

1: You need to include <string>, not <cstring>.

2: The constructor of a class must have the same name as the class itself IIRC. construct_player() should be renamed to just player() or, if you want construct_player() to be a regular function member, you must give it a return type (such as void).

Obviously, if you change construct_player() to become the constructor of player(), you can't call the constructor explicitly so the line
"new_player.construct_player();"
must be deleted.