I am fairly sure just like the NES, Sega didn't stop shipments until sales stopped, which could have been even longer then the NES. And maybe they are including the 3rd party sales.

Yeah probably, the SNES is at 22.88 M in the US whereas the highest reliable source for the Genesis in America I can find is 20 M in March 1998.

From the same Famitsu source Soundwave used we can see the Sega Genesis shipments from 88/10 to 94/3. Also thanks to Sega Retro for the sources,

This leads to a total of 3118 or 31.18 million by the end of March 1996. By 1997 it seems that Sega has stopped producing Genesis consoles and sold the rights to Majesco. The source at the bottom estimates that 400,000 Genesis were sold in North America in 1997 and then Majesco projects to sell another 1.5 million in 1998. I can't seem to find a solid source on Brazil numbers but it has to be a few million at least and it probably would not be included in the Famitsu numbers.

So now the question is where did the 20 M figure in this article come from? Well this is just a guess but looking at EA's UK figures, it seems that the Genesis peaked in 1994 and sales slowed down, this matches the drop in Famitsu data. Perhaps the NYTimes estimated the American sales from the same Famitsu source we're using or they had access to NPD data.

A note on NPD data for 16 bit consoles:

You can find a summary here for Genesis (along with other consoles) NPD data from 1994 to 2001 based on a 2004 report. I do not think this data is very reliable and what stood out to me was that the the Nintendo figures did not match Nintendo's consolidated sales report. So if Nintendo's numbers do not match then I also suspect the Sega numbers. If you add up the Famitsu American Genesis numbers up to 94/3 and then add on the NPD numbers till 1998 then the total comes out to about 19.4 million, close enough to match the NYT report. There was also a revised Wedbush document in 2014 that put the American Genesis total at 18.5 million, again the Nintendo numbers do not match the consolidated report so take these numbers with a grain of salt.

Also this is hearsay but apparently the Genesis won four Christmas seasons against the SNES. Looking at the graph until 96/03 the two consoles were pretty neck-in-neck so it's possible this was the case, also note that the graph combines the US with Europe.

So let's break this all down:

Japan: 3.93 M
Brazil: 2-4M(?)
Europe (Till 94/3) - 8.6 M
USA (Till 94/3) - 12.80 M
Europe + USA (94/4 - 96/3) - 5.85 M
1997 NPD USA - 0.40 M
Majesco Projections - 1.5M
Unaccounted 1996 figures - 1-2 M(?)

Total: 33.08-39.08

This means that outside of Japan the Genesis sold between 29.15M and 35.15M while the SNES sold 31.93M. So it's anyone's guess who won the West in the end.

Joe Miller who was the Sega of America VP of Product Development did state in a 2013 interview that he thinks the Genesis ended up breaking just over 40 million. If you added up the Nomad all the Genesis models, Nomad and "others" but not including the Majesco products. I am not quite sure what he meant by "others" here (unless if he misspoke?) but I think he might be referring to the Sega CD and 32X which would add another 3 million to the total. Anyways who knows where he got his figures from so I would take this with a grain of salt.

Sources:

89-94 Shipments
95 Shipments
96 Shipments
1997, 1998, 1999
Wedbush
Interview with Joe Miller

Edit:

So a little bit of an update. I went through this GAF thread about console sales data and read this interview with TecToy about Genesis sales in Brazil. From the interview I found that they ended up selling 3 million in Brazil by the time of the interview, in the thread apparently Sega sold 8 million in Europe by 1997 (which is when the console was discontinued) and I was able to find some revised NPD data after and including 1994 and add it up with the Famitsu data up to 1994. So breaking it down again...

Japan: 3.58 M
Brazil: 3 M~
Europe: 8M~
US: 20M~

Total: 34.58M~

So I think it's safe to say that the Genesis did not sell 40 million consoles, but the actual number will always be a mystery. I think Joe Miller's 40 M statement could still be true if you add up all the add-ons and Sega Nomad....maybe....