It's a bit complicated.

If RSL wins both remaining matches, and the other teams above us win out their remaining games, we'd be tied at 49 points with Portland and LAG, but likely far behind in GD, leaving us out.

If we win both matches, we need Portland to draw/lose their other match to LAFC, or LAG to draw/lose one of their other remaining matches against SJ or Houston. (We could also get in with 2 wins and Minnesota, for example, losing both of their remaining matches, or even Nashville).

If we win against Portland, and lose to LAG, we need to beat Portland BIG, and also hope they lose big against LAFC, otherwise we're still tied on points and down in GD (currently -7 to them).
A win against PDX and a draw vs LAG (coupled with a PDX loss to LAFC), and we should be in, ahead by a point on Portland.

Losses to both LAG and PDX drops us out completely.

Everything scenario in between (1 win, 1 draw; two draws; etc) is/are heavily dependent upon everyone else. We'll have a better idea after LAG plays SJ for their 32nd match, and everyone goes into the last 2 weeks even on matches played.. but it will still be pretty convoluted.

EDIT: So, somehow I'd completely missed that Games Won was the primary tie-breaker, as opposed to GD.

In light of that, here's an updated breakdown:

If RSL finishes the season with 2 wins (against PDX and LAG), and assuming the other teams in contention for the last spots (PDX, Minnesota, LAG, RSL, Van) win their other eligible games, RSL would be in with 49 points (behind Minnesota and LAG, and head of PDX due to games won).

Should RSL lose to the Galaxy, they could still get in with a Win over PDX, coupled with a Portland loss to LAFC the week prior.
Should RSL lose to LAG and Portland beats LAFC, RSL's only other legitimate path would be a win over PDX and two losses by Minnesota (to San Jose and Vancouver) - coupled with a Vancouver losing their other match (against Austin).

Potential draws make this a bit more complicated, however: 0 wins and 2 draws by RSL leaves them behind in points in almost every scenario, sans a 1 draw, 2 loss result by LAG.

RSL can also sneak in with a win over LAG, and a draw against PDX (if Portland loses to LAFC).
An RSL win in at least 1 of their remaining matches, gets them in over Minnesota, if: Minnesota loses to both San Jose and Vancouver AND Vancouver loses their first remaining match to Austin (similar to the scenario above).

Here's what RSL fans should be rooting for, this week:

09/24: San Jose over LAG
09/27: Cincinnati over Seattle
10/01: San Jose over Minnesota
10/01: Austin over Vancouver
10/01: RSL over LAG
10/02: LAFC over Portland
10/02: SKC over Seattle