Derailleur play between cage and knuckle
How worn are the cassette and chains? How old is the shifter cable. 

In my experience the order of things that cause shifting issues are chain wear, cassette wear, cables first. In my mind these are all considered consumables and replaced regularly. Derailleur hanger, especially if unknown history, is a likely suspect 

Last is derailleur itself.  At 10000km on a Claris it past its 'economic life', so I would not be worried about replacing it.  The play in the video is a bit more than I would like, but I hesitate to say it is definitely the cause of your shifting issues.