You are not populating your Game array correctly.  You are trying to call the Player() constructor as if it were a regular class method (which it is not), and worse you are calling it via an uninitialized Player* pointer.
You need to use the new operator instead, eg:
class Game
{
private:
    int maxPlayers;
    Player** playersArray;
public:
    Game(int aMaxPlayers);
    ~Game();
}
Game::Game(int aMaxPlayers)
{
    maxPlayers = aMaxPlayers;
    playersArray = new Player*[maxPlayers];
    for(int i = 0; i < maxPlayers; ++i)
        playersArray[i] = new Player; // <-- here
}
Game::~Game()
{
    for(int i = 0; i < maxPlayers; ++i)
        delete playersArray[i];
    delete[] playersArray;
}
A safer option is to use std::unique_ptr instead of raw pointers:
#include <memory>
class Game
{
private:
    int maxPlayers;
    std::unique_ptr<std::unique_ptr<Player>[]> playersArray;
public:
    Game(int aMaxPlayers);
}
Game::Game(int aMaxPlayers)
{
    maxPlayers = aMaxPlayers;
    playersArray = std::make_unique<std::unique_ptr<Player>[]>(maxPlayers);
    for(int i = 0; i < maxPlayers; ++i)
        playersArray[i] = std::make_unique<Player>();
}
That being said, there is no need to use an array of Player* pointers when an array of Player objects will suffice instead:
class Game
{
private:
    int maxPlayers;
    Player* playersArray;
public:
    Game(int aMaxPlayers);
    ~Game();
}
Game::Game(int aMaxPlayers)
{
    maxPlayers = aMaxPlayers;
    playersArray = new Player[maxPlayers];
}
Game::~Game()
{
    delete[] playersArray;
}
Or:
#include <memory>
class Game
{
private:
    int maxPlayers;
    std::unique_ptr<Player[]> playersArray;
public:
    Game(int aMaxPlayers);
}
Game::Game(int aMaxPlayers)
{
    maxPlayers = aMaxPlayers;
    playersArray = std::make_unique<Player[]>(maxPlayers);
}
Which you can then simplify further by using std::vector instead:
#include <vector>
class Game
{
private:
    std::vector<Player> playersArray;
public:
    Game(int maxPlayers);
}
Game::Game(int maxPlayers)
    : playersArray(maxPlayers)
{
}