Sure, let's create a test case generator for the problem "Memory Match."

The generator will need to produce multiple datasets, each consisting of an even number \( N \) between 2 and 1000. The input ends with a zero, which is not part of the actual datasets.

Here's the test case generator code:

```python
import random

def tcgen():
    # A function to generate a single dataset
    def generate_dataset():
        N = random.choice([2 * i for i in range(1, 501)])  # Ensure N is even
        return N
    
    # Generate a list of datasets
    datasets = []
    num_datasets = random.randint(1, 10)  # Number of datasets to generate, can be adjusted
    
    for _ in range(num_datasets):
        datasets.append(generate_dataset())
    
    # Append the terminating zero
    datasets.append(0)
    
    return datasets

# Example usage:
test_case = tcgen()
for n in test_case:
    print(n)
```

### Explanation:

1. **`generate_dataset` function**:
    - This function generates a single dataset value \( N \), ensuring it is an even number between 2 and 1000. It does this by choosing a random integer \( i \) between 1 and 500 and then multiplying by 2.

2. **`tcgen` function**:
    - Generates a list of random datasets by calling `generate_dataset` a random number of times (between 1 and 10 in this example, but you can adjust this range as needed).
    - Adds a terminating zero at the end of the list to indicate the end of the input.

3. **Example usage**:
    - Calls `tcgen` to generate the test case and prints each value in the resulting list, including the terminating zero.

This generator will produce random valid inputs as specified by the problem statement, ensuring that all conditions are met.