About nothing changes. They had already won the Super Bowl after the 99 season. So I guess they earn a little cred as a Dynasty of sorts; bonus point for winning it a 2nd time in 3 years with a different coach than their first time.
The Rams had a great 5 year run from 1999 through 2003.
97 - Vermeil as Coach - 5 and 11 record (GM: Dick Vermeil)
98 - Vermeil as Coach - 4 and 12 record (GM: Dick Vermeil)
99 - Vermeil as Coach - 13 and 3 record; win the Super Bowl (GM: Dick Vermeil)
00 - Martz as Coach - 10 and 6 record; lose in 1st round of playoffs (GM: Charley Armey)
01 - Martz as Coach - 14 and 2 record; lose the Super Bowl (GM: Charley Armey)
02 - Martz as Coach - 7 and 9 record (GM: Charley Armey)
03 - Martz as Coach - 12 and 4 record; lose in the 2nd round of playoffs (bye in the 1st round) (GM: Charley Armey)
04 - Martz as Coach - 8 and 8 record (GM: Charley Armey)
05 - Martz fired mid season - 6 and 10 record (GM: Charley Armey)
06 - Linehan as Coach - 8 and 8 record (GM: Jay Zygmunt)
The organizations next winning season and playoff appearance: 2017 (as LA Rams).
With the nature of the salary cap and the brutal nature of attrition that is an NFL season and an NFL career, having a non-losing season for multiple consecutive seasons (let alone deep runs in the playoffs) is really, really difficult.
Winning Teams have losing teams vulturing Free Agent talent off of them in the off-season. Teams already paying prime dollars for existing stars have less money because of the salary cap to spend to keep their own talented drafted players who become Free Agents themselves after their first 4 or 5 (in the case of first round picks) years in the league. AND, drafted players become more expensive to a degree as they progress from year 2 to 3 to 4 (and to 5) and their annual salaries automatically increase per the collective bargaining agreement.
And NOT just players, but coaches too get vultured. Assistant Coaches on Playoff Teams get offered Coordinator jobs on other teams (Pro or college). Coordinators get offered head coaching jobs.
And players age and get hurt. Football is not pattycake.
The Marshall Faulk of ages 25 - 27 when he came in 2nd-1st-2nd in MVP voting with 2200, 2400, and 2100 yards from scrimmage of the 1999-2001 seasons was not the same Marshall Faulk who gained 1500, 1100, and 1100 yards from scrimmage at ages 29 and 31. And certainly not the Marshall Faulk of age 33 who was no longer playing in the NFL.
It seems pretty obvious that Dick Vermeil built the Rams into the winning Team that it was 1999 through 2003; even though he left after 1999 when he won the Super Bowl.
And it appears that Charley Armey the new GM and Mike Martz the new Head Coach (formerly the Offensive Coordinator) after Vermeil retired were good enough to keep a good thing going as long as could be reasonably expected with the talent on hand and what they could do via the draft and Free Agency. But, they were unable to continue success beyond expectations because they (and their successors) were unable to reload with either A) SuperStar Franchise QB; or, B) quality cheap players acquired in the rookie draft (oh, and the better season you have, the farther back in each round you draft).
Best Players drafted by Armey/Martz (per Career AV as calculated by pro-football-reference)
2000 - 30 AV - Tackle John St Clair in the 3rd Round (traded away after 2 seasons)
2001 - 58 AV - Defensive Tackle Ryan Pickett in the 1st Round (departed as FA after 5th Season and played another 8 years) (Oh, and STL had 3 1st round picks that year)
2002 - 25 AV - Defensive Back Travis Fisher in the 2nd Round
2003 - 41 AV - Linebacker Scott Shanle in the 7th Round (cut after 1st season)
2004 - 75 AV - RB Steven Jackson in the 1st Round
2005 - 78 AV - QB Ryan Fitzpatrick in the 7th Round (and all of 135 pass attempts in his 2 years with Rams) & 62 AV for Guard Richie Incognito drafted in the 3rd round (who got traded mid-way through his 4th season with the Rams)
And now freaking Jay Zygmunt becomes GM (before he had technically been the GM's boss as President of Operations) and as GM is now fully in charge of the draft for the Rams (or at least in charge of the department that evaluates/chooses the college players in the draft)
2006 - 13 AV - Defensive End Victory Adeyanju (plays 4 years for the Rams and then is out of the NFL)
2007 - 22 AV - Defensive End Adam Carriker
The Rams clearly lacked the front office talent and organizational culture to become anything other than what they became OTL. Which wasn't bad in the Martz/Armey years. It just offered no path forward once the benefits of the Vermeil years finally aged out.
I don't see how winning a 2nd Super Bowl in 2001 is going to change any of that.
Georgia Frontiere did not die until 2007/2008. No change in organization/culture is going to happen until after her death and the rise of a new ownership. Alas, the cast of Ram's mediocrity had already been set by that point.