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One possible way to create a counting game for coin flipping in C++ using data structures is as follows:

1. Define a coin-flipping function that returns either "heads" or "tails" randomly.
2. Create a vector data structure to store the results of the coin flips. This vector should have a fixed size equal to the number of flips the user wants to play.
3. Prompt the user to enter how many times they want to flip the coin and store this value as an integer variable.
4. Use a loop to flip the coin the specified number of times and store the results in the vector.
5. Use another loop to count the number of times "heads" and "tails" appear in the vector.
6. Display the results to the user.

Here's an example implementation:

#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>

using namespace std;

// Function to flip a coin and return "heads" or "tails"
string flipCoin() {
    if (rand() % 2 == 0)
        return "heads";
    else
        return "tails";
}

int main() {
    // Seed the random number generator with the current time
    srand(time(NULL));

    // Prompt the user for the number of flips
    int numFlips;
    cout << "Enter the number of times you want to flip the coin: ";
    cin >> numFlips;

    // Create a vector to store the coin flip results
    vector<string> flips(numFlips);

    // Flip the coin and store the results in the vector
    for (int i = 0; i < numFlips; i++) {
        flips[i] = flipCoin();
    }

    // Count the number of heads and tails
    int numHeads = 0;
    int numTails = 0;
    for (string result : flips) {
        if (result == "heads")
            numHeads++;
        else
            numTails++;
    }

    // Display the results to the user
    cout << "Out of " << numFlips << " flips, there were " << numHeads << " heads and " << numTails << " tails." << endl;

    return 0;
}

This program uses a vector to store the results of the coin flips, and then counts the number of heads and tails using a loop. The results are then displayed to the user.