Camshaft pulley slack

I bought a DX engine sometime ago, but haven't mounted the pulleys until now.  Just noticed that there is a lot of play in the pulley when it is mounted on the camshaft. There's also some wear on one side of the slot for the woodruff key. This is my first time working on an engine, so could anyone tell me if the play is something to worry about and if my camshaft is bust? Hopefully you can see the movement on the video

Looks about right to me as you don't have it bolted or torqued.  The wobble is normal for one that is just hanging there to me.

As Briano1234 said stick the bolt in and torque it up, I use a long bar in one of the holes of the cog and a clean bit of wood on the top of head (cam cover removed) to hold the cog still when tighten the bolt.

Make sure you have the cog on the right way round as it’s got the timing marks on it and will go on either way round….

Once all done up feel for any play…

The reason I got a bit alarmed was that the pulley on the oil pump had zero slack in it, it was all snug over the woodruff key. There is also some slight wear to one of the edges of the slit in the cam, where the woodruff key sits. I guess it will tighten up once I torque it, so if you are saying it's not a problem I will go with that.