Your analysis is incorrect (though perhaps not in the way you'd think!):

ProPublica, in line [36] of their analysis, fit a Cox proportional hazards model on pairs (score, race) with three possible scores (low, medium, high) and six possible races (Caucasian, African-American, Asian, Hispanic, Native American, and Other). Thus there are 18 total groups; each person belongs to exactly one. This model tries to estimate the relative risk of recidivism for each of these groups. The "base rate" cancels out when you fit this model, so these risks are all expressed relative to a baseline; this baseline is chosen to be (low, Caucasian).

There are 17 degrees of freedom here. It doesn't matter what basis you choose (as there is no regularization), so all that's really happening is you're counting recidivism in 18 buckets. The basis ProPublica's formula chooses is 2 = 3-1 terms for score, 5 = 6-1 terms for race, and 10 = (3-1)x(6-1) terms for the "interaction"; this reflects their choice of coding using two categorical variables. But you may as well just have 17=18-1 terms each of which expresses the relative risk between each group and the baseline; this would be the equivalent of coding using one categorical variable for the entire pair. The advantage of such an expression is it'd be harder to make the mistake both you and ProPublica make: the "interaction" terms are not the droids you're looking for!

In the "Background" section of your "How to lie without statistics" article, you write: "the size of the second coefficient (relative to the first) is directly proportional to the degree to which the old predictor was biased". The first coefficient is the coefficient in front of the "old_predictor" variable (here, "score_factorHigh/Medium"). The second coefficient is the coefficient in front of the "is_black" variable. I'm honestly surprised, given how clearly you seem to write here, that you then focus on the wrong coefficient later.

The relevant coefficient is the one on "race_factorAfrican-American"! That coefficient is 0.27879 and very significant. In other words, the algorithm is "biased in favor of blacks". To be ever more precise, the numbers you're actually looking for are "race_factorAfrican-American + race_factorAfrican-American:score_factorHigh" and "race_factorAfrican-American + race_factorAfrican-American:score_factorMedium"; as one would expect, the interaction terms are correction terms that aren't the dominant effect.

Your error is a bit more understandable given quite how much ProPublica messes up line [37]. They forget the race terms entirely!! The correct calculation for "Black High Hazard" is exp(0.27879 + -0.18976 + 1.28350) = 3.95 and "Black Medium Hazard" is exp(0.27879 + 0.84286 - 0.17261) = 2.58; note that I included the race terms! Their sentence should read "High risk white defendants are 3.61 more likely than low risk white defendants [to recidivate in a given time period], while High risk black defendants are 3.95 more likely than low [risk white defendants...]". (They wrote 2.99 for the italicized term. For medium risk, they give the numbers as 2.32 white versus 1.95 black instead of the correct 2.58 black.)

To specifically isolate where your analysis is incorrect: two of your three conclusions are incorrect. Conclusion #1 is correct. Conclusion #2 is not: the analysis directly suggests that it is biased in favor of blacks and the interaction term is not the dominant effect. Conclusion #3 is also incorrect: that term is how much more likely (low risk, African Americans)s are to recidivate than (low risk, Caucasian)s. If blacks had a much higher recidivism rate but it was fully captured by the score, this term would be zero!