In Highlander, the Demoman's main job is dealing high amounts of damage. His weapons are great at dishing out large amounts of damage to crowds of players and slow, high HP targets. However he lacks the ability to reliably protect himself from close range threats (most often from the Scout), so he is often paired up with the Heavy and Medic to form the core of a Highlander team. He serves a similar role to his 6's counterpart of dealing damage and leading up uber pushes, but he is also expected to deal with sentry nests.
The Demoman is most traditionally part of the Highlander Combo, alongside the Medic, Heavy, and oftentimes a Pyro. When using the Ubercharge he will often lead the push. Depending on the situation, the Demoman may share the Uber with another class, or just take the whole Uber. In a defensive situation, a team may forgo a Demoman Uber in favor of keeping the Pyro and Heavy alive to slow down a push. If the Medic is using the Kritzkrieg, the Demoman is nearly always the primary recipient. A common practice is "Sticky Sniping", which has a Demoman charge up a sticky bomb, then taking the Kritz right before shooting the sticky into a crowd. If done correctly, the critical sticky will catch the enemy team off guard and secure a few picks or an Uber drop.
Stickybomb traps, while not as useful as in less-organized formats, do provide the Demoman with an Area Denial and Picking tool. However, due to the the number of Area Denial and Picking classes that are always present in a Highlander game, this mechanic is not as useful as in 6v6. The one major downside to a sticky trap is that one cannot sticky jump. When a trap is not up, however, sticky jumping is a very potent tool for the Highlander Demoman. It allows him to quickly respond to threats, act quickly off of advantages, and cover distance much faster than a majority of classes on the field.
The Demoman's primary jobs in Highlander are to put out damage and survive. The Demoman has the highest DPS in the game, and because his primary weapons are explosive, he can deal large amounts of damage to groups. Typically the Demoman gets a lot of frags because he can put out so much damage, but oftentimes he relies on classes like the Scout or Soldier to clean up the damage and finish off targets. Because of his damage output, the Demoman is one of the most important classes.
As the Demoman's stock weapons are one of the most powerful among all the weapons in TF2, Demomen rarely deviate from the stock loadouts. Alternate options are often not as good and lower the Demoman's damage capability; the Loch'n'Load projectiles dish out more damage than normal grenades, but it has only three grenades in a clip, and the Scottish Resistance's prolonged sticky activation time make it hard to use the stickies in an attacking fashion. A notable exception is the Pain Train, which doubles the Demoman's capturing speed, which allows for a more aggressive playstyle.
Some teams and players have experimented with playing Demoknight, which refers to playing Demoman with one of the shields (the Chargin' Targe, the Splendid Screen or the Tide Turner) equipped in place of his Sticky Launcher. This strategy is reliant on using a turning script that allows a charging Demoknight to turn at a greater rate than what the game normally allows. However, the Tide Turner doesn't need a turn script and refills its charge meter on kill, making it a popular choice for competitive Demoknights. The Demoknight results in a playstyle similar to a Roamer, which is centered around getting key picks. This playstyle has not yet been proven to be an effective alternative to stock Demoman, because of stock Demoman's versatility.