Put mayonnaise, chili sauce, parsley, onion, horseradish, worcestershire, and kosher salt and freshly ground black pepper to taste into a medium bowl and stir well to combine; set Russian dressing aside.
Butter rye bread, then flip over and spread each slice with about 1 tbsp. of the dressing. Top 4 of the bread slices with 2 slices swiss cheese, ½ cup sauerkraut, and ¼ lb. corned beef each. Top each of those slices with 1 of remaining slices of bread, dressing side down.
Heat a large skillet over medium heat and, working in batches if necessary, add sandwiches in a single layer. Cook, flipping once and occasionally pressing the sandwiches down with a wide metal spatula, until golden brown and crisp on both sides, about 10 minutes total. Serve immediately.