As Icebuster mentioned, there are two different flavors of 64 bit Arduino IDE, each with their own download link on the Software page:
- "Linux 64 bits" - this is the one for use on x86-64 bit architecture host machines
- "Linux ARM 64 bits" - this is the one for use on ARM architecture host machines
If you try to use the ARM one, you will get this "exec format error".
It's not necessary to run the install script, so this is not the cause of your problem. I never use it. I just extract the downloaded file and run arduino.