In terms of direct impact on the Rams, it's all about the draft (I'm just going to skip the potential for the Rams to face one of these teams in the Super Bowl...). All three teams are sitting at 5-6, so there's definitely plenty in the draft order to sort out.
If you need some historical perspective to reinforce how important that is, consider this. In 2006, the Ravens took Haloti Ngata off the board with the 12th overall pick. Three picks later, the Rams selected would-be All-Pro CB Tye Hill.
In 2003, the three teams were all within the 10th and 16th picks. At 10, Baltimore picked up Terrell Suggs. At 16, the Steelers added Troy Polomalu. In between the two at 12th, the Rams picked up Jimmy Kennedy.
The year prior, the Steelers got five-year starting guard Kendall Simmons with the 30th pick. One pick later saw the Rams grab LB Robert Thomas. Both missed out on the Ravens' selection at 24, soon-to-be Hall of Famer Ed Reed.
The implications of draft order are easy to parse in hindsight.
In foresight, it's obvious that there will be implications to be had.
Try and mentally bookmark tonight's game for next April. It'll likely have a small, but definite, impact on the future of the Rams.