Does building stamina running also build stamina for every other exercise?

It will keep you from running out of breath because it works your heart, but it won't help your other muscle groups.

To a certain extent, but considering some other exercises use different muscle groups, you won't have the same stamina doing exercises that make use of muscles not used much in running.

Yes, but only partially. Building stamina improves heart, circulatory, lung function. That improves fitness, with an improvement in stamina overall. But, this improves stamina only partially in other exercises. That is because it doesn't necessarily train other muscle groups.

Suppose you train to a level where you can jog 15 miles a day. If you then go for a long distance swim, even at a slow pace, you could expect your shoulder and arm muscles to tire. You have not built stamina for your arm and shoulders.

By the way, if you are able, I recommend building up endurance.

Your cardio is transferable to other activities but each activity uses slightly different muscles so there is always an adjustment period when you try a new activity.  However you will likely adjust faster than someone who is inactive.