Sniper (Highlander)
As that Highlander is a format with 1 of each class, both teams will have one sniper at all times. Being both a boon and a bain to a teams existence.
Primary Responsibilities
Getting Picks
It's usually up to the Sniper, or one of the other "pick" classes such as Scout, Spy, or Soldier to initiate a conflict. To either begin a push or simply making sure that a push doesn't begin. It can not be emphasized enough that this, and this alone is the biggest responsibility of a Sniper, and most other responsibilities are directly tied to this.
Counter Sniping
Perhaps it's wrong to say this is one of Sniper "primary responsibilities", but it will happen quite often. Snipers tend to have great sight-lines that usually end up where both of them can see each other, typically snipers attempt to shoot each other in order to achieve Pick Responsibility, and also in killing the other Sniper they open up opportunities for themselves.
Area Denial
Snipers can effectively shut down entire attack lanes with their innate ability to one shot nearly anything in game with proper preparations. Snipers can make sure cart lanes and control points are clear, or flanks are kept down.