The Lenovo y580 seems to be the best perfomance one, with an i7, better GPU than the other 2, and GDDR5. In general looks like a good deal, and will give better gaming performance than the other two. (Assuming I see the correct y580, your link got parsed wrong http://www.gaminglaptopsjunky.com/lenovo-ideapad-y580-15-6-gaming-laptop-209945u-i7-3610qm-cpu-gtx-660m-2gb-gddr5-gpu-8gb-ddr3-1600mhz-500gb-hdd-fullhd-display-999-lenovo-site/). As long as you don't mind spending the extra money for more performance, go for this one. It also appears to be pretty rugged, which is common for lenovo's I believe.
Between the other two, I think the HP should be better gaming. I don't think the i7 will be worth losing the GDDR5 on the GPU. But neither of the two is a bad laptop, and really you could throw the decision either way based on other features you want, quality, or brand preference.
edit: Though the HP looks like it's a 2nd gen i5, which will be a little less powerful and use more battery.