The system uses the NFL's official disabled list to update players' injury status.
MANAGING YOUR INJURED RESERVE
Players who are eligible for the injured reserve (IR) are designated with an asterisk and an "IR," followed by a number indicating expected duration (in days) of the injury in red. To move a player on your team to an IR slot click on the "Manage IR" link at the top of your team page. This link will only appear in leagues which use IR slot(s).
What confuses me about that is that the NFL's official designation of "IR" means "Out for the season". But I don't think that's what the above is saying. Do you take this to mean that if a player is officially "Out" for the week, ESPN will let me put that player in an IR spot? What about those listed as "Doubtful"?