Play in rear wheel hub I've got some play in the rear wheel hub, which makes the wheel move sideways a bit. Here's a video: https://drive.google.com/open?id=1EpXNE9YYdzwxotgWbCeWi2DM9FOlmY7A

How can I fix this? Do I have to disassemble the hub?
Your hub looks like a serviceable cup and cone types, so you will be able to fix the problem.

You will have to disassemble the hub, but it is not a difficult procedure. You will need some special tools - a chain whip and cassette lock ring tool to get the cassette off, and possibly a cone wrench.

There are many resources available online that can guide you such as this Park Tool Company article.

You may need to simply adjust the bearings, but you should check the amount of  wear on each bearing component and replace if necessary.