Yes, venison is red meat.
Depending upon your dog's nature (and your feeding philosophy), red meat may or may not be necessary. If you wish to feed only "fast twitch" animals (rabbit, chicken, rodent, smelt, sardine) vs "slow twitch" (cow, pig, large fish (grouper, not tuna)) to keep your dog lean, it is not necessary to feed ANY red meat. BUT, you must feed liver and other organs to have a balanced diet. Just feeding a certain cut of meat over and over will not provide the variety needed for a complete and balance diet.
Re the issue of Omegas: It is a long and politically charged topic. Here's a little "light" reading: http://en.wikipedia.org/wiki/Omega-3_fatty_acidhttp://www.nlm.nih.gov/medlineplus/druginfo/natural/993.html
What IS known: animals eating a natural diet have more Omega 3s than those fed unnatural diets (for bovines natural would be grasses, for example, rather than corn and soy mixed pellets fed on feed lots). Therefore, if you are feeding meat that has been fed an "unnatural" diet, you will need to supplement with Omegas.
Now, regarding the term "fish oil"...You are going to have to investigate what the manufacturer means by "fish oil". Not all fishes are created equal. You can see from the Wiki page a list of Omega 3 concentrations for each type. Depending upon the average depth that they live, their bodies will have more or less Omega 3s. The deeper the water and the colder the water, the more omega 3s because they are more flexible and therefore remain liquid in lower temps than the longer chain Fatty Acids.
Some of the other things to consider is the length of the food chain:
Krill oil is the most green of the non plant producing Omega 3 sources, but it is very expensive.
As you move up the food chain, there is a greater likelihood of heavy metal contamination, which is bad.
But the FDA says the risk is worth the benefit, so that might be good. (Then again the FDA is a political machine, so you need to consider the source.)
You can always feed Flax or Hemp oils, although they will also have plant estrogens, which may be bad ...esp, for the boys.
Is this helping?
I feed Grizzly Salmon Oil. It suits my budget and the fact that my dog is old, so we probably won't have to worry about heavy metal issues. In younger dogs, where brain development might be an issue, I'd choose to feed Krill over Salmon.