Well, it doesn't. I also thought that it should work. The whole internet is full of text that gen2 card should work in gen3 slot, but then after a lot of searching I found some posts where was said that gen3 have some different voltages or something than previous gens and is why it could be the case of not always being backwards compatible.
As I said the card itself works fine on other other mobo with gen2, pity I don't have gen3 card to test.
Using motherboard's onboard graphics for now, but I must find out why it is not working and is it really the case of different PCI-E generations.
By the way here are other system specs:
Motherboard: GA-H97-HD3 (1.0)
BIOS Ver: H97-HD3 F4
GPU: GV-N440D3-1GI
CPU: Intel Core i5-4460
Operation System: Win 8.1 64-bit
RAM: Kingston 16GB
Power Supply: 500W
Storage: Kingston SSD 120GB