So these animations are only showing you a quarter of the picture. It's a plot of the absolute value of the Electric field. It doesn't tell you anything about the direction of the field, nor does it show the Magnetic field.

So for the dipole, all it is is two straight wires, about a quarter wavelength long connected to a transmission line. Imagine the top connected to the center of the coax, and the bottom connected to the shield.

When a wave coming down the coax hits the antenna, it causes a current in the wires. Electrons will be pushed into the top wire and pulled out of the bottom wire. This creates a charge on the wires, negative on top, and positive on the bottom, and you can see that in the animation.

But because waves reverse, soon you'll get a reverse current and the top will become positively charged and the bottom negatively charged. This can happen billions of times a second for something like 2.4GHz wifi.

And also, current creates a magnetic field. So when current is flowing in the wires, there is a magnetic field wrapping around them. This current hits zero when the wires are fully charged, and is at it's maximum right when the wires are neutral.

So now you have Electric and Magnetic fields all swirling around each other at a constant frequency. This is you get EM radiation.

If I haven't lost you yet, you should consider going to school for electrical engineering; antenna theory is some of the most esoteric shit this side of Quantum Mechanics.