The Von-Richter reaction's accepted mechanism is given by-
As you can see, this is not a simple case of say, removal of $\ce{NO2-}$ ion, instead it involves removal of $\ce{N2}$ which provides thermodynamic stability.
the tables you use have been calculated on the basis of $\ce{pK_a}$ values which don't give the right answers in many cases due to solvent effects and the intermediates involved in specific reactions. Wikipedia itself states
It is important to note that the list given above is qualitative and describes trends. The ability of a group to leave is contextual. For example, in $S_nAr$ reactions, the rate is generally increased when the leaving group is fluoride relative to the other halogens. This effect is due to the fact that the highest energy transition state for this two step addition-elimination process occurs in the first step, where fluoride's greater electron withdrawing capability relative to the other halides stabilizes the developing negative charge on the aromatic ring. The departure of the leaving group takes place quickly from this high energy Meisenheimer complex, and since the departure is not involved in the rate limiting step, it does not affect the overall rate of the reaction
This order is a general trend and as the mechanism in this reaction suggests, is not the end-all be-all determining factor.
Coming to why this reaction gives low yield, is mainly due to the hydrolysis of $\ce{CN-}$ ion by water/alcohol to $\ce{HCOO-}$/$\ce{CH3COO-}$. This is was suggested because according to this paper$^1$
the recovery of much
unreacted starting material suggest that hydrolysis (or alcoholysis) competes
with the nitro compound for cyanide ion to the extent that hydrolytic destruction of cyanide is the yield-limiting factor; it is known that cyanide ion is rapidly
hydrolyzed in water solution at elevated temperatures
There is one thing missing from wikipedia that von-richter reactions were conducted in elevated temperatures and in sealed tubes $(\ce{150^oC-165^oC})$ both originally by von richter himself and in subsequent studies for mechanism*.
There may be other competitive side reactions but were not documented for this reaction (because it is of low yield anyway, there was not much work on it.)
*The paper by J.F.Bunnett,J.F.Cormack and Frank C.Mckay$^1$ (linked by @waylander) cites-
von Richter’s reactions were run in “alcohol” solution in sealed tubes at $\ce{180^oC-200^oC}$ or higher.
and the letter by Prof. Myron Rosenblum $^2$ while explaining the mechanism
with evidence from isotopic labelling cites-
9.5 mmoles of p-chloronitrobenzene, when treated
with 20 mmoles of potassium cyanide, and 6.2
mmoles of ammonium nitrate in a sealed tube at $\ce{160^oC}$ for
1.75 hours, gave nitrogen gas containing 0.75%
$\ce{N_2^29}$
It is normal for nucleophilic $S_nAr$ to be conducted around this temperature** so this is not surprising thing to be missed by wiki, it also means that $S_nAr$ of cyanide on bromine can probably be competitive but experiments predict a majority of unreacted products according to this table in most solvent cases:
interestingly both this table and the letter by Prof. Rosenblum (46.5% yield for the same reaction but with chlorine) suggest different yields to what wikipedia suggests.
TL;DR : Leaving group order doesn't matter here because of different mechanism involved converting $\ce{-NO2}$ to $\ce{-N2-}$ which is a very good leaving group and yield is low because of hydrolysis of $\ce{CN-}$ ion at the preferred temperature.
**Ref :. Morrison & Boyd sec 26.7 (Nucleophilic aromatic substitution: bimolecular displacement)
cited material:
$1$ : J.F.Bunnett, J.F.Cormack and Frank C.Mckay ,"Mechanism and reactivity in aromatic nucleophilic substitution reactions"J. Am. Chem. Soc. 1958 5(3), 481-490 doi 10.1021/jo01149a007
$2$ : Rosenblum, M. The Mechanism of the von Richter Reaction. J. Am. Chem. Soc. 1960, 82, 3796–3798; doi 10.1021/ja01499a090
