Other non-TAR shows that I can think of at the moment:
1. Lost (2001)
All teams are stranded somewhere and have to make their way to the finish line. There are no eliminations.
2. Race Across The World (2019-2020, Season 3 halted because of COVID-19)
Mostly similar to Lost, but preserves the TAR structures of having checkpoints, legs and 1 elimination over 2 seasons.
3. World's Toughest Race: Eco-Challenge Fiji (2020)
4. ローカル路線バス乗り継ぎの旅 and 太川蛭子の旅バラ (2007-2020)
Not exactly reality TV, but it features 2 male celebrities and a female guest finding the best route possible to travel between 2 points in Japan while travelling on local buses that do not use the highway. In some episodes, there were some deviations, where they travel by train and the goal is to visit landmarks near certain stations.
Not aired so far: Race To The Center Of The Earth (2020)
Three more:
5. Treasure Hunters (2006):
Think putting TAR & National Treasure in a blender. Teams of three travel across the US, France, and England as they follow clues leading them up to the grand prize of $3,000,000 dollars. This show did a split start before HaMerotz LaMillion 4 did!
6. Expedition Impossible (2011):
Teams of three travel through the Sahara Desert and Atlas Mountains in Morocco to win $150,000 to split and a new car for each team member. This show had more of the extreme challenges like rappelling, hiking tough terrain, etc.
7. Peking Express (2004-present):
This show started in the Netherlands and feature teams of two hitchhiking from Russia, Mongolia, and China with only a euro a day. It later expanded to other European countries (Most notably France & Spain). Most first seasons of the show followed the Russia -> Mongolia -> China format, but then expanded to more countries. Most notably the second seasons of the show traveled in China, Nepal, and India.