Aarseth very simply defines cybertexts as textual 'machines'. A machine does not have to be a computer, it is merely (or only) a procedure to allow different 'texts' to be produced.
The "I Ching" is a cybertext, for here you throw three coins and use a table of symbols (six continuous or broken lines) so that any query can produce on of 4096 possible 'texts'. (Though if we include the question as a part of the text then while there are 4096 responses there are an infinite number of texts.)
Other non computer examples include the work of Oulipo (a French literary movement that combines mathematics with textual production), where Raymond Queneau's "a hundred thousand billion poems" is "a sonnet machine book of 10 x 14 lines, capable of producing 10(14) sonnets, and Marc Saporta's 1962 novel which came loose leaf and you composed the order yourself.
Obviously there are many computer examples of cybertext, including Joyce's "Afternoon" and Moulthrop's "Victory Garden". A database could be a cybertext (not all databases are cybertexts, since they are often used to store simple information - personal records for instance), but Aarseth also argues that MUDs and MOOs are cybertexts, as are, in some instances, computer programs themselves, and of course many types of digital games are also clearly cybertexts.
While a cybertext is any mechanical process that produces texts (and this mechanical process is a part of the textual activity) this is only one part of what Aarseth is describing. This is because this idea of the cybertext concentrates on the 'machine' end of the text, of what 'makes' the text come to be. But of course the reader also has a role to play.