Season steak with salt, pepper and Old Bay. Preheat a greased grill pan or griddle over medium-high heat. Grill the meat, turning it occasionally, for 12 minutes. Transfer the meat to a cutting board and let rest for 10 minutes. Thinly slice against the grain. Wipe off the grill pan and turn the heat to low.
Meanwhile, rinse the sauerkraut and squeeze out the excess liquid. In a medium saucepan, heat the sauerkraut over medium heat.
In a small bowl, stir the sour cream, ketchup, relish and horseradish. Season with salt and pepper.
Butter 1 side of each bread slice; spread mustard on the other side. Build each sandwich starting with a bread slice, buttered side facing out, then 2 cheese slices, some watercress, sauerkraut, steak, homemade Russian dressing and another bread slice, buttered side out. Grill the sandwiches to melt the cheese. Serve with the chip alongside, passing extra sauerkraut and dressing at the table.