Australia indeed doesn't issue physical visas, but registers your passport for admission in a given status. This can be checked by airport check-in staff.
On 1 September 2015, Australia ceased issuing visa labels to holders of Australian visas. Australian visas are issued and recorded electronically. All visa records are stored in a central database which enables online checking of visa details by visa holders, registered Australian organisations and airline staff. Your visa is linked to your passport or ImmiCard through its unique identification number. You and other parties need this number when checking your visa online.
Also, Timatic, the database used by check-in staff, says:
Note: Australia issues many visas electronically, including
those for visitors, students, temporary business entrants
and working holiday makers. There is no visa label contained
in the passport, existence of an electronic visa, and
therefore authority for airlines to board passengers, is
verified by airlines using Australia's Advance Passenger
Processing (APP) system prior to boarding and by immigration
officials on arrival in Australia. Travelers are responsible
to ensure that they have a visa to enter Australia.
While you may want to print the confirmation E-mail for your own comfort, you're not expected to show it to anyone.