Bring 6 quarts of water to a boil and add about 2 tablespoons salt.
In a 12-inch saute pan, saute the garlic in the olive oil over moderate heat until lightly brown, about 1 minute. Add the chiles and continue cooking about 30 seconds longer. Add the wine and butter and boil over high heat for 3 minutes. Add the shrimp stirring until just cooked, about 4 minutes. Season to taste with salt and remove from heat.
Add the spaghettini to the boiling water and cook according to package instructions, until tender but still al dente. Drain the pasta and add the spaghettini to the saute pan with the shrimp. Place the saute pan back over medium heat. Stir gently until the spaghettini is coated with sauce, then toss in the arugula. Stir quickly to combine and arugula just wilted, about 30 seconds. Check the seasoning and transfer the pasta to a large serving bowl. Serve immediately.