No, actually it does. Socialism is a redistribution of wealth and resources based on a cooperative approach to management. In the NFL's case, there is a salary cap and revenue sharing. The league agrees to a lucrative TV contract and then splits the profits between all 32 NFL teams.
What Empire was saying with the Giants and Packers is correct. If the NFL was run like the MLB, then the teams from large media markets and deeper pockets would benefit greatly.
The NFL decided that the "sink or swim" attitude would only lead to a lack of parity and fairness in the league. When you look at baseball, teams like the Pirates have not been relevant for a while because they cannot compete financially with team in their own division, let alone the rest of the league.
Just because something is profitable doesn't mean that it is capitalist. Socialist countries still have private businesses and personal wealth. The difference is, the ceiling is closer to the floor.