Nvidia made GPUs before DirectX was even thought of, though that's not relevant here. Also, only Windows supports DirectX - you can't use it on Linux, Mac OS, or any of the mobile OSs, and it's only really useful for gaming. A GPU without DirectX is perfectly usable for many purposes.
Nvidia says it supports DirectX 12, though:
http://www.geforce.com/hardware/desktop-gpus/geforce-gt-620/specifications
I suggest you try installing the drivers direct from
Nvidia's website, though I'm guessing you've already tried that.
If that doesn't work, you may need to remove any other display drivers. Try
this tool, then reboot and re-install the Nvidia drivers.
If all else fails, you may need to reinstall Windows.
Note that the War Thunder minimum requirements say that you need at least a 7800GT; GTX 460 recommended. Our
GPU hierarchy doesn't seem to have the GT620, but it says the GT630 is slower than the 460 and only a little faster than the 7800GT. Your GPU simply may not be fast enough - it's not really a 'gaming' card.