I don't hunt big game, so I'm not really up on the caliber
requirements for effectively bringing them down. I'd imagine,
however, that shot placement is as important, if not more so, than
the caliber of the projectile fired. In other words, a smaller
caliber projectile hitting a vital organ is probably more likely to
bring down an elk or deer than a large caliber projectile
penetrating only flesh.
In most states, the Department of Natural Resources sets minimum
caliber requirements for different categories of game. For example,
here in Minnesota, the various rifle and pistol calibers authorized
for hunting big game are listed here. As you can see, the list of legal
cartridges is quite long!
The guy in the blue windbreaker and red earmuffs is shooting a
lever-action rifle, most likely chambered in 30-30
Winchester.
With regard to the SKS, the 7.62x39 cartridge is on the list of
approved big game cartridges, so I would assume it is capable of
bringing down deer. I have colleagues who hunt deer in Wisconsin
with SKS rifles using readily-available hollowpoint ammo.