Thank you for your reply.
I think that the spirit of this article is to say that for the recreationally pilot (casual sports pilots), that only wants reliability in his engines, it is sufficient the improving that produce nitro metane at 5% due to the effect of reducing octane .( at least this was my interpretation )
On the other hand , about the oxigen and the increment in power that nitromethano gives, I agree with you, and the article do not denied that.
The nitromethane has two effects:
To contribute oxigen to increase power.
To act like cetane improver, at least when is used at 5%.

We do not want (and we can not) to replace the nitro methano in the effect of increasing power,
we only want to improve reliability in the engines increasing the cetane value, that it is the more important effect that produce the nitromethane in the range of 5%.
We have tried with methyl nitrate at 5%, and the engines had erratic running. Due to that, the range of use it is in small quantities.
( like the common range of use of cetane improvers in diesel engines 0.1-0.3%)
The cetane improver decompose to generate free radicals which enhance the initiation of combustion. You do not need necessarily oxigen to do it.

About the phrase from the article:
"Nitromethane isn't added to sport fuels to provide power."
I understand the following in the context of the article:
Nitromethane is not added at 5% to increase power (you need a tach to detect rpm increase).
Nitromethane is added in this proportion to provide smooth idle and running and starting easy.
If you are a "performance pilot", of course, you need to increase % and then you will have to much power.

You are right, we do not have instrument to quantify the improvements in acceleration and running that we say that happens, but
We have the most subjective of the instruments:
The feeling of 5 pilots in several models.( one of them has more than 40 years of esperience and is not senile).
Any way, is imprudent of my part, to affirm things without parameter quantification, sorry.