You do not need a smartphone to play Magic, the MTG Companion app is only recommended :) As long as you have registered your DCI number online in the past, you are good to go! If you don't remember what email you used to register your DCI number, you can find out here: https://accounts.wizards.com/
-Greg
Just a slight note on this! If you've registered your DCI number online in the past and have an associated email for your Wizards Account, you are indeed all good to go. However, if you have a Wizards Account and no current DCI number (say for example, if you're new to tabletop events after already creating a Wizards Account for MTG Arena), you're also good to go. Going forward, your Wizards Account will be what matters!
Wizards Community Team
Just a slight note on this! If you've registered your DCI number online in the past and have an associated email for your Wizards Account, you are indeed all good to go. However, if you have a Wizards Account and no current DCI number (say for example, if you're new to tabletop events after already creating a Wizards Account for MTG Arena), you're also good to go. Going forward, your Wizards Account will be what matters!