Update and review
I used it, and it worked pretty well, it put a medium-large 5x4 bull elk down, and I can't complain about that! I used it because I had to this season, but I don't think I'll use it again for elk.
Distance for the first shot was 100 yards. The bullet entered behind the shoulder broadside, producing a quarter sized hole going in, shredded both lungs, and produced a much smaller hole - almost a slit - when it exited between the ribs through the other side.
The elk paused for a second, and then ran directly toward me before breaking left and running hard back toward the dark timber he'd emerged from. That gave me a chance to take a follow-up broadside shot at about 60 yards. That second bullet entered high above the shoulder and severed the elk's spine, causing him to pile up hard; the bullet expanded nicely and blew out a 3" solid chunk of spine.
I'd give the bullet a "C+" grade. It performed well enough to kill the elk, but I don't like how the exit wound on that first shot was much smaller than the entry wound. That bullet may have keyholed going out. There was no evidence of jacket-core separation, but I've used bonded/monotholic soft points that have performed better on the exit. I'm not sure that the game king would have exited had it hit a rib on the way out, and I'd like a bigger hole for an exit wound. I think the first bullet, that shredded both lungs - would have killed the elk eventually, but I didn't want him to get back to that dark timber, so I took a second shot. Elk are tough.
In conclusion, the 165 grain .308 Winchester Sierra gameking btsp will kill an elk, but I'll be switching to a 165 bonded/monolithic sp bullet next year for more reliable performance in case I hit heavy bone like a shoulder or rib.
Edited to add: and to be fair to Federal, the company suggests the 165 btsp gameking round for use on medium-sized game (mule deer and deer), so kudos to Federal for making a round that did do the job on a 650 pound bull elk!