I don't see the 'Allow Apple Watch to unlock' option.

Hello Russbude!

Here are the instructions you will need to follow in order to enable the ability to unlock your Mac with your Apple Watch. I will also provide the link to the Apple Guide from which the instructions are derived, this way you will have access to the guide for future reference. Best of luck!

Unlock your Mac with Apple Watch

If you have a Mac (2013 or later) with macOS Sierra, your Apple Watch can instantly unlock your Mac when it wakes from sleep. You need to be signed in to iCloud using the same Apple ID on both your Mac and Apple Watch.

To use Auto Unlock, you need to have a passcode set for your Apple Watch—open Settings , tap Passcode, tap Turn Passcode On, then follow the onscreen instructions.

Turn on Auto Unlock. On your Mac, choose Apple menu > System Preferences, click Security & Privacy, then click General. Select the “Allow your Apple Watch to unlock your Mac” checkbox. If you don’t have two-factor authentication turned on for your iCloud account, follow the onscreen instructions, then try selecting the checkbox again.

For more information about two-factor authentication, see the Apple Support article Two-factor authentication for Apple ID.

Unlock your Mac. While wearing your watch, just wake up your Mac—no need to type in your password.

Tip: Make sure your Apple Watch is on your wrist and unlocked.

https://help.apple.com/watch/#/apd4200675b8?cid=acs::applesearch

Hi,

If you've truly followed all steps, then you probably don't have watchOS 3 installed on your apple watch.

Check if you have OSwatch 3 on your watch:

Settings > General > About >> scroll to Version (I had 2.2.2)

If you do have version 3, double check that all the steps on how to enable this have truly been followed.

To update apple watch to OSwatch 3:

Open the Watch app on your phone >> General >> Software Update

Remember, the watch must be charged at least 50% or be connected to its charger.

Once the watchOS has been updated, you should see the tickbox.

Hi,

I have the same problem and know the cause; the early MacBook Pro has an 802.11n ethernet adapter. You need at least an 802.11ac adapter.

You can buy them on Ebay or some other retail site for a few bucks and it's plug and play in your Mac.

You need a mid 2013 or later Mac you said you have a early 2013 Mac.

System requirements for Continuity on Mac, iPhone, iPad, iPod touch, and Apple Watch - Apple Support

The Mac Help points out a way to check this using the System Information:
"System Information can confirm if your Mac supports Auto Unlock. Choose Apple menu > About This Mac, then click System Report. In the sidebar, click Network, click Wi-Fi, then look in the Interfaces section for Auto Unlock."

So, when in doubt, look at the system profile  > About This Mac, System Report and check the Network > Wi-Fi section, if the the installed card type for your network supports the Auto Unlock feature.