Cut the ribeye into 16 equal 1-inch cubes. Place steak and mushrooms into a gallon zip-lock bag.
In a medium bowl, whisk together all marinade ingredients until the sugar is dissolved. Pour over the steak and mushrooms. Seal the bag and toss to coat. Refrigerate for at least 30 minutes and up to 2 hours.
While the steak marinates, wash the potatoes. Place them in a large saucepan, cover with 1 inch of water, and bring to a boil. Cook for 5 to 7 minutes until just barely fork-tender. Drain and set aside.
Assemble the kabobs by threading onto each skewer in this order: steak, potato, steak, mushroom, steak, potato, steak, mushroom. Repeat with remaining skewers until all ingredients are used.
Preheat grill to medium-high heat. Lightly oil the grates.
Grill kabobs for 5 to 6 minutes per side, turning every 3 minutes, until the steak is cooked to your preferred doneness and potatoes are nicely charred.
Remove from grill and let rest for 1 to 2 minutes before serving.