How did Siri know where this plane was going?
Actually this is nothing new and isn’t all that creepy (although I suppose that depends on what you consider to be creepy).

Siri has been closely integrated with the WolframAlpha Computational Knowledge Engine for many years now. 

To determine where a plane flying overhead is going, Siri only needs to send a request along the lines of flights seen from current geoIP location to WolframAlpha. WolframAlpha then returns the details to Siri, such as where the flight is going, the flight number, type of plane, altitude, etc. 

For this to work you must already have Settings > Privacy > Location Services switched on - so if you have any concerns about revealing your location then you should check these settings and which apps you're sharing your location with.

If you're interested in learning more about WolframAlpha, you can refer to Wikipedia’s WolframAlpha entry. This provides a great overview, including the fact that other devices (such as some Android devices) also use it.

In summary: Apple isn't spying on you. All that is happening is your iPhone is sending its geolocation to WolframAlpha which in turn is using data provided to it from another third party to return the flight information back to Siri. This is nothing new and some Android devices can also do the same thing.