How to have the OS launch applications at startup time?
It really would be nice to have some startup manager shipping with the system, which lets the user decide what to start and what not. But that's not the case, it works a bit different:

Apps with the "run at startup" permission can register a "listener" for the BOOT_COMPLETED broadcast ­– which the system always issues on that event. This way they get notified of that event, and can decide to perform some action. That could be starting some background service which keeps running – but they could also do something little and then exit again.

IMHO Skype has an option to automatically log you in after boot, so you're available for incoming calls. AFAIR that's even the default behavior of the app. If there's no background service running for that, it might register for some cloud messaging then – which again would "wake it up" to deal with incoming calls. That way the app had no need to permanently run in background. Indeed the app also declares the com.google.android.c2dm.permission.RECEIVE permission (C2DM stands for "Cloud 2 Device Messaging", which now is GCM = Google Cloud Messaging), so this could be the explanation.



UPDATE:

Andrew T. confirmed this in the comments:


  I finally checked the Android manifest of Skype by opening its APK file (base.apk), and indeed there is com.skype.android.push.DeviceBootReceiver with intent filter android.intent.action.BOOT_COMPLETED. I didn't investigate what it's doing though. Also, I forgot that broadcast receiver is not listed under running process as John mentioned (I can confirm this being a developer). So, you're correct on your guess :)