A gyre is another name for a swirling vortex. Ocean gyres are large swirling bodies of water that are often on the scale of a whole ocean basin or 1000 s of kilometers across (hundreds to thousands of miles across).
Lean meats are meats with a relatively low fat content. Skinless chicken and turkey and red meat, such as pork chops, with the fat trimmed off are examples of lean meat.
While no research that I could find looked specifically at game meat in terms of health risks or benefits, based on their nutrition profile, they can be considered a good source of lean protein that can be consumed in moderation as part of a healthy diet along with skinless poultry, fish and trimmed lean meats.