Montenegro is a tiny country, still relatively new to international competition after the fall of the Soviet Union. There are not a ton of basketball players to draw from and the competition in Europe is steep, even among countries in the former Soviet Union.
None of that mattered. It did not really matter that Montenegro was no favorite to win Eurobasket in 2011 or 2013 or 2017 (they missed out in 2015), this was a big moment and a big appearance for the team.
Nikola Vucevic was at the center of it. You could easily argue that Montenegro missed Eurobasket, the championship for European teams, in 2015 because Nikola Vucevic had a falling out with the national team coach.