Why is a gas furnace vented but a gas dryer is not?
Your gas dryer vents its combustion products outside along with the moisture from your clothes, so it is vented to the outside.

Your oven doesn't vent out mostly for sake of having limited combustion. There are ventless heaters available. However you run it, though, any natural gas burning device will create water vapor and carbon dioxide. If it malfunctions, you also risk it producing carbon monoxide. Stoves and ovens get by because they have relatively low BTU output and in a residential setting relatively low use. In a commercial setting, you'd achieve exterior venting with a ventilation hood.

When you get to devices with higher output such as a clothes dryer or furnace, you really want that out of the house. The impracticality of venting your stove, though, outweighs the relatively small amount of downside.