You should provide some codes to help understand your issue.
I’ll guess here that you want to display in each category the users who play the game. So you need first to assign to each player the category they play. In the register_taxonomy function, this is done by adding 'user' in the second parameter.
As they’re is no automatic UI to assign categories to user (that I know of), you need to add your own by using multiple hooks
//when editing another user profile (e.g. for admin)
add_action('edit_user_profile', 'my_user_display_edit_form');
//when editing your own profile
add_action('show_user_profile', 'my_user_display_edit_form');
//when creating a new user
add_action('user_new_form', 'my_user_display_edit_form');
//when saving another user profile (e.g. for admin)
add_action('edit_user_profile_update', 'my_user_save_meta');
//when saving your own profile
add_action('personal_options_update', 'my_user_save_meta');
//after a new user as been created
add_action('user_register', 'my_user_save_meta');
I leave the implementation of my_user_display_edit_form and my_user_save_meta to you. (see wp_get_object_terms() and wp_set_object_terms() documentation)
Then you can get a list of users ID by term using get_object_in_term() coupled with get_users()
$ids = get_object_in_term($term_id, $taxonomy);
$users = get_users(['include' => $ids]);