Each AA alkaline battery may be 2800 milliamp hours at 1.5 volts. That's 2.8 amp hours. So eight of them will put out 12 volts, but it will still be a 2.8 amp hour pack.
For practical purposes, the voltage will drop to unusable levels by the time the pack is about half exhausted, so really about 1.4 amp-hours at the relatively high drain of a half ampere load. They probably should not be loaded to more than a half amp, which is 500 milliamps. At that load, they will last about three hours.
The way alkaline batteries work, they last longer and will put out more total energy at very low drain. At high drain rates, they get hot and die quickly. Some type of rechargeable battery would be much better, sealed lead acid, nickel-metal hydride, lithium-ion, or the more expensive lithium iron phosphate.
The game cam probably has only a small fraction of an ampere of drain unless it is actively taking pictures. A 12 volt regulated power supply of the correct polarity with the proper tip would be your best bet.
This would work great, but you could buy a lot of AA batteries for the cost.