Under Vladimir Putin, Russia has increasingly embarked on an aggressive foreign policy designed to undermine Western interests, this includes invading Georgia, annexing Crimea, funding and arming sepratists in Eastern Ukraine, and intervening militarily in Syria to prop up the regime of Bashar al-Assad. The authoritarian nature of his presidency which has focused on rebuilding of Russia's military capabilities, including increasing its nuclear weapons stockpile, only reaffirms the relevance and need for NATO as an effective deterrence.
Russia under Vladimir Putin is not the Soviet Union. The current military threat of Russia is overstated and far less adventurous than the Cold War era. Russia's own military doctrine states that the biggest threat to peace is the military build up amongst NATO member states and the expansion of NATO membership to its border. Russia's foreign policy is one of self-defence.
[P1] Russia still has an aggressor role in global politics. [P2] Therefore, NATO is still relevant.
Rejecting the premises
[Rejecting P1] Russia's role is one of self-defence, not aggression.