I know this card would not run right, those 4 screws, just like cpu hold downs are critical. They have to be torqued max, and evenly. AMD cards usually employ spring loaded screws, I notice Nvidia cards with their big heat spreaders sometimes don't. The load probably is spread across the gpu die easier with a bigger surface area.
For all we know, the hole is not tapped in the heat sink in that corner, I have heard of that happening.
Could also be a million other reasons there is no screw there, none of them good.