What do greenhouse gases have in common with carbon dioxide that makes each of them a greenhouse gas?

To begin with, carbon dioxide is a greenhouse gas just like the others.

Second, I'll just copy and paste the response I previously gave to this question.

The solar radiation heats the Earth, but it also heats the atmosphere. The solar radiation comes in all kinds of wavelengths, but most of it is known as short wave radiation.

Depending on the wavelength and type of matter, all energy will interact with it. For example, x-rays with very short wavelengths will pass through most materials, but will be stopped by lead and calcium.

Here's where things get interesting: in the case of the Earth and Sun, shortwave radiation reached the surface of the planet without much interference from the atmosphere, heats the planet, and then radiates energy of its own that is longer in wavelength than the incoming solar radiation and is sensible heat (that is, heat that humans can feel).

Short wave radiation entering the atmosphere is largely unaffected, but long wave radiation leaving the atmosphere is affected. This is because greenhouse gases, such as carbon dioxide, methane, and water vapor, are transparent to short wave radiation but opaque to long wave radiation. In essence, they function similarly to a greenhouse's glass walls, which let light in but keep heat out.

Both greenhouse gases and carbon dioxide have the ability to absorb and emit infrared radiation, which traps heat in the Earth's atmosphere, contributing to the greenhouse effect.

Greenhouse gases, including carbon dioxide, share the property of being able to absorb and emit infrared radiation. This property allows them to trap heat in the Earth's atmosphere, contributing to the greenhouse effect and resulting in global warming.