It is highly recommended players use Magic: The Gathering Companion but, it is not required.
Players who do have Companion can streamline your event registration by inputting the code at the top of your event through the Join Event option. They will show under the Expedited Players, ready to be enrolled when the event begins.
Manual event registration is still possible without Companion. Simply record a player's Wizards Account email and they will be enrolled. Players who do not have a Wizards account can be directed to https://myaccounts.wizards.com/register to create one.