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It is not. The title of your linked article is "What Gorbachev heard" - why speculate instead of asking him? Gorbachev, Shevardnadze, Yazov and other top USSR officials have all said that there was no such thing. Gorbachev even went on to explain why it couldn't have been even in theory: democratically elected leaders can't give any promises beyond their term limits. Shevardnadze, the foreign minister of USSR at the time, gave a lengthy interview[1] where he described how the soundbites you quote were related to German reunification and have been taken out of context. His successor Kozyrev, the first foreign minister of the Russian Federation, has been even more direct and called people who keep pushing this narrative idiots. In 1990, nobody in USSR's leadership expected the USSR and Warsaw Pact to collapse in such a short time, let alone negotiate how Europe would look like afterwards. It simply does not fit the timeline nor the way diplomacy is conducted. It's a textbook example of a hoax.
Beyond that, whatever happened in 1990 was superseded by a written treaty between NATO and Russia in 1997, before anyone from Eastern Europe was admitted, in which Russia reiterates the "respect for sovereignty, independence and territorial integrity of all states and their inherent right to choose the means to ensure their own security".[2] Back then, Russia was still receiving food aid from the US, and was in no position to make any demands. The rewritten version of history that has that fictional promise at its core was invented in mid-2000s.
[1] https://www.spiegel.de/international/europe/interview-with-e...
[2] https://www.nato.int/cps/en/natohq/official_texts_25468.htm