Shifting gears requires you to dismount the bike and move the chain by hand, often taking 30 seconds - 5 minutes to do the change. The upside is that you retain ALL of the benefits of a fixie or single-speed — it remains a rock-solid drivetrain.
Sometimes a 1x2 or 2x1 gear configuration with manual-gear-changing is considered a dinglespeed. For these, it's sometimes possible to shift while in motion, at least in one direction. (I would think this takes some care. There are no limiting screws here, and pushing the chain off the other side would be very easy?)
Once you add the tensioner, it can no longer be a fixed-gear bike, it can only be single-speed. Tensioners can't withstand the pressure needed to brake using backwards force.
The 1982 Huffy Pro Thunder Z2 took this approach, with two gears and a deraileur up front, and a tensioner in back.