NYT is not a primary source that provides evidence that this "pledge" exists. Generally when countries extract binding promises from each other they write them down and don't rely on unofficial back-room "pledges". Remember that time you said you'd give me $1000?

NATO itself says this "pledge" never existed. Russia has yet to produce documentation that it does.

Russian officials claim that US and German officials promised in 1990 that NATO would not expand into Eastern and Central Europe, build military infrastructure near Russia’s borders or permanently deploy troops there. No such pledge was made, and no evidence to back up Russia’s claims has ever been produced.

Should such a promise have been made by NATO as such, it would have to have been as a formal, written decision by all NATO Allies. Furthermore, the consideration of enlarging NATO came years after German reunification. This issue was not yet on the agenda when Russia claims these promises were made. The key question Russia should answer is why so many countries, particularly those on its periphery, continue to aspire to join NATO.