Activation

From a third-party IMEI checker, such as the website illustrated in your screenshot, this could mean almost anything - or nothing.

imeicheck.com will likely be accessing public or carrier provided databases of devices sold (or registered) by Cellular Carriers.

Apple’s official warranty checker can be found here:

Check Your Service and Support Coverage - Apple Support

There is no service or website you can use to reliably determine that. I guess you’ll find out when you get it. Hopefully, you purchased it using a service that provides some kind of buyer protection in case it is and the seller refuses a refund.

Here is what Apple suggests when purchasing a previously used device…:

Check for Activation Lock before you buy a device from someone else

Before you buy an iPhone, iPad, or iPod touch, from someone other than Apple or an authorized Apple reseller, make sure that the device is erased and no longer linked to the previous owner’s account. Follow these steps to check if the device is ready to use: 

1. Turn on and unlock the device. 
2. If the passcode lock screen or the Home screen appears, the device hasn't been erased. Ask the seller to completely erase the device by going to Settings > General > Reset > Erase All Content and Settings. Don't take ownership of any used iPhone, iPad, or iPod touch until it's been erased.
3. Begin the device setup process.
4. If you're asked for the previous owner’s Apple ID and password, the device is still linked to their account. Hand the device back to the seller and ask them to enter their password. If the previous owner isn't present, contact them as soon as possible and ask them to use a browser to remove the device from their account. Don't take ownership of any used iPhone, iPad, or iPod touch until it has been removed from the previous owner’s account.

You will know that a device is ready for you to use when you're asked to "Set up your iPhone," “Set up your iPad," or “Set up your iPod” the first time you turn it on.

As such sites are notoriously inaccurate, what are you hoping to determine by checking there?