Is it possible while using the Ruby version manager to run scripts not from the console but using other ways — at system startup or by a keyboard shortcut for example?
RVM installs a command rvm-shell. You can use rvm-shell, pass it whatever you would pass rvm use, then you can execute a shell command.
rvm-shell will set your environment for that shell script, or you can use rvm-shell on one line, and have it execute the parameter as a shell command.
For example:
rvm-shell rbx-2.0 -c 'which ruby'
Which should equal your rbx ruby.