Heat oil in the pot of a multi-functional pressure cooker (such as Instant Pot(R)) on the Saute setting. Saute onion, carrots, and garlic until onion is translucent, about 5 minutes. Add red wine.
Lay venison into the pot; top with 1/2 the butter. Mix in salt, pepper, and red pepper flakes. Add crushed tomatoes. Close and lock the lid. Select the Stew setting according to manufacturer's instructions; set timer for 20 minutes. Allow 10 to 15 minutes for pressure to build.
Bring a large pot of lightly salted water to a boil. Cook orzo in the boiling water, stirring occasionally until tender yet firm to the bite, about 11 minutes. Drain and stir in the remaining butter.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Remove venison and cut into bite-sized pieces; meat should be fall-apart tender. Mix venison back into the pot. Serve the ragout over the orzo.