Add the olive oil to a heavy-bottomed pot or deep-sided large skillet. Heat over medium-high heat. When the oil shimmers and starts to smoke lightly, add the venison.
Season the venison with salt and black pepper. Cook until the meat is nicely browned. Stir often for even browning.
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, scraping up any brown bits from the pot.
Add the remaining red wine, tomatoes, vinegar, mustard, ketchup, and sugar. Stir to combine.
Partially cover with a lid. Adjust the heat until you achieve a gentle simmer. Cook until the mixture has slightly thickened. This can take up to one hour.