In Mountain Goats you work to move your goats to the top of 6 different mountains where they can score points as long as they stay there. You can share spaces with other goats on the way up, but there is only room for one goat at the top of each mountain. If someone else's goat moves to the mountain top, they will kick you off and you'll have to start your trek over.
It's a game about timing. You need to not just get to the top of the mountain, but get there when no one else is in position to knock you off.
It's a game about keeping your eye on your opponents. Maximizing your score, but also making sure you don't let anyone else score too much.
There is the fun chance to knock each other off the mountain. But it doesn't feel too mean because you can only knock back goats that are in a scoring position, and it isn't a huge setback. It is just a normal part of the cycle of the game.