Works for me:
$ composer require google/apiclient:^2.0.0@RC
$ php -r 'require __DIR__ . "/vendor/autoload.php"; var_dump(Google_Service_Calendar::CALENDAR_READONLY);'
string(49) "https://www.googleapis.com/auth/calendar.readonly"
With this in mind, your startup is probably ruined. Give it a try composer dump-autoload.
Otherwise, you may be dependent on an older version of the API client that does not have this class. Try:
$ composer show -i | grep apiclient
google/apiclient v2.0.0-RC4 Client library for Google APIs
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