Does banana plugs such as this:
will fit just fine with this ports:
If they don't fit, is there an adapter of some sort that will make them fit?
Additional question: What do you call this classic speaker ports anyway?
As the other answers have said, banana plugs will not fit. However, so-called “pin” plugs are designed to fit speaker jacks, and a little searching suggests there also exist adapters from banana plugs to pins, though as a much more obscure item; here's an unfortunately unavailable example which nicely shows the difference in size between banana plugs and pins:
The groove in the pin allows it to be held firmly by the jack.
Caution: Many pin plugs have uninsulated metal bodies. They may short to each other when placed in the closely-spaced jacks shown in your pictures. Make sure to use insulated plugs or wrap them in insulation such as heat-shrink tubing.
They won't fit by themselves, but you can make your own with a short cable that has a female banana plug jack. Just cut that cable and stick the wires in to the slots and then you have an adapter. Alternately, you could cut off the banana plugs on the original cable, but if you don't want to damage it, then my adapter suggestion will work.