Laracasts/Integrated actually provides their own specific API. It isn't very full, but if you need more you can use $this->session to access the underlying instaclick/php-webdriver. You can read more about that library in its docs, but the gist is that it basically uses Selenium's JSONWireProtocol as is. This requires sending arguments in a JSON-like array syntax.

Putting that together, you should be able to get this done something like:

public function test_add_poi_from_fleet_map(){
    $this->doLogin('test','test')
        ->click('#showMap')
        ->wait(5000);
    $this->session->moveto(['element' => '#mapContainer', 'xoffset' => 100, 'yoffset' => 100]);
    $this->session->click(['button' => 2]);
    // (button 2 is right click according to JSON wire protocol)
    $this->see('Add Point of interest');
}

(If you want to be able to chain those commands, you could create your own helper functions that return $this at the end. Then you could also collapse the arrays into traditional arguments if you prefer.)