Looks like they did not include the creation of the counter in the program but instead are handling it on the Client side using System Program. Take a look at the tests:

const allocIx: TransactionInstruction = SystemProgram.createAccount({
            fromPubkey: payer,
            newAccountPubkey: counter,
            lamports: await connection.getMinimumBalanceForRentExemption(COUNTER_ACCOUNT_SIZE),
            space: COUNTER_ACCOUNT_SIZE,
            programId: PROGRAM_ID
        })

This is a little different than how they've implemented in the anchor example, where they've explicitly created an initialize function in the program:

pub fn initialize_counter(_ctx: Context<InitializeCounter>) -> Result<()> {
    Ok(())
}

Looks like they did not include the creation of the counter in the program but instead are handling it on the Client side using System Program. Take a look at the tests:

const allocIx: TransactionInstruction = SystemProgram.createAccount({
  fromPubkey: payer,
  newAccountPubkey: counter,
  lamports: await connection.getMinimumBalanceForRentExemption(
    COUNTER_ACCOUNT_SIZE
  ),
  space: COUNTER_ACCOUNT_SIZE,
  programId: PROGRAM_ID,
});

This is a little different than how they've implemented in the anchor example, where they've explicitly created an initialize function in the program:

pub fn initialize_counter(_ctx: Context<InitializeCounter>) -> Result<()> {
    Ok(())
}

Looks like they did not include the creation of the counter in the program but instead are handling it on the Client side using System Program. Take a look at the tests:

https://github.com/solana-developers/program-examples/blob/d6cd69d8df3eb95966b3d2361ede84529413567a/basics/counter/native/tests/counter.test.ts#L37C8-L43

This is a little different than how they've implemented in the anchor example, where they've explicitly created an initialize function in the program: https://github.com/solana-developers/program-examples/blob/d6cd69d8df3eb95966b3d2361ede84529413567a/basics/counter/anchor/programs/counter_anchor/src/lib.rs#L11-L13

Looks like they did not include the creation of the counter in the program but instead are handling it on the Client side using System Program. Take a look at the tests:

const allocIx: TransactionInstruction = SystemProgram.createAccount({
            fromPubkey: payer,
            newAccountPubkey: counter,
            lamports: await connection.getMinimumBalanceForRentExemption(COUNTER_ACCOUNT_SIZE),
            space: COUNTER_ACCOUNT_SIZE,
            programId: PROGRAM_ID
        })

This is a little different than how they've implemented in the anchor example, where they've explicitly created an initialize function in the program:

pub fn initialize_counter(_ctx: Context<InitializeCounter>) -> Result<()> {
    Ok(())
}