I've had a few people report this now, so it definitely warrants some further investigation.
Is this with Dropzone 4? Also, what macOS version? If you untick the 'Start Dropzone at login' checkbox in the preferences and re-tick it then reboot does it start? The way the launch at login works it wouldn't be expected to show under the user accounts login items section, so that's as expected.
It would also be great to see what Console log messages are being recorded. If it still doesn't start after unticking and re-ticking the 'Start Dropzone at login' checkbox then rebooting then would you mind opening Console.app which is in /Applications/Utilities and doing a search for 'Dropzone' and then unticking the 'Start Dropzone at login' checkbox and re-ticking it and then pasting me any relevant log messages. Thanks!