Add the olive oil to a heavy-bottomed pot or deep sided large skillet. Heat over medium-high heat. Season the venison with kosher salt and black pepper. When the oil shimmers and starts to smoke lightly, add the venison. Work in batches if necessary to achieve a golden brown crust on the meat. Remove the deer meat from the pot and set aside. Reserve the oil in the pan.
Reduce the heat to medium. If the pan looks dry, add more olive oil as needed. Add the onions and garlic for around 2 minutes while stirring. Add the chili powder, cinnamon, cumin, coriander, allspice, paprika, dried thyme, and tomato paste. Cook while stirring for 1 minute.
Add about one cup of the red wine to deglaze the pot. Stir with a sturdy wooden spoon or spatula while scraping up any brown bits in the pot. This will take about one minute.
Add the remaining red wine, tomatoes, vinegar, mustard, ketchup, and sugar. Stir to combine.
Partially cover with a lid. Cook over medium-low heat or at a slow simmer until the mixture has thickened to your liking. This can take up to one hour.