Give your dad a pint!
The Yankees did not score despite making four hits in each of the nine innings. For example, lead man gets a hit, second hitter hits into a double play: now there's two out and three empty bases. The next three batters each get a hit (bases are now loaded). The next two batters strike out. Four hits, no runs.
There's more than one way to score a run without getting a hit, or a walk, or drawing an error. The key is that an 'error' is defined as a fielding error. If the pitcher hits the batter, or if it's a passed ball, it's not counted as an error. (I believe that's also true of a wild pitch or a balk.) So, the first Braves batter reaches base on a passed ball. On the next pitch, the runner at first base steals second. On the next pitch, the runner steals third base. On the next pitch, the batter hits a sacrifice fly, and the runner scored. The pitcher throws a no-hitter, there are no errors and no walks, but his team still loses.