Ok.. I dragged out an ancient Express.. plugged it into the network.. and I think you have got the wireless setting wrong..
You cannot have the express plugged into ethernet AND set to join or extend wireless at the same time.
Here is mine set to join a wireless network..
And this is with ethernet.. and wireless turned off.. it must not be turned on.
Notice the dotted line when connected via wireless becomes solid with ethernet.
So go into the setup by clicking the Edit button..
And turn off wireless.
Airplay should then work fine.
If you wish to switch over you must go to edit and fix the wireless configuration.
Click on update at the bottom and continue..
Wait until the LED on the Express starts flashing and remove the ethernet plug.
I did leave ethernet in to see if I got the same effect as you.. and got stupid results..
It does not show an error but the Express was flashing Amber and was clearly having issues..
Once I removed ethernet and restarted the Airport Utility it settled back again.
If you still have trouble start over with a reset.. press and hold the reset button on the express with a pin for about 10sec .. then start from scratch.
STRONGLY recommend NOT using Apple recommended names. All names should be short, no spaces and pure alphanumeric. Passwords same rules but can be longer.
Mine has airplay working.
Where does your wireless name, Time Capsule Wi-Fi Network come from??
No TC is showing up in the Airport Utility.. if that is from old setup.. reset and start over.
BTW.. Thanks for the screenshot.. I did not know there was a firmware upgrade for the A1264 Express.. so that is helpful.