I searched Google, but I can't find a similar error anywhere, so I'll ask here.

I'm trying to install ZeroTier and after uploading file and rebooting the following error appears in the logs: can not install zerotier-7.14: system-7.14 is not installed, but is required

My router is RB5009 running RouterOS 7.8. Architecture of the downloaded file is good, ARM64. This has to be something else.

Is it a joke?

Try to install it on RouterOS 7.14, like the message in your log says.

P.S: upgrade your router first! 7.14 is newer than 7.8, this is not primary school math, versions are not decimals