Are device administrator permissions a security risk? I would like to use t-igra's SwipeLock+ app, but it requires device administrator permissions.

Google Play Store lists the following permissions:


receive data from Internet
view network connections
full network access
run at startup
draw over other apps
prevent device from sleeping
install shortcuts


Are any of these a security risk?
To answer your title, device administrator by itself is not a risk as it does not give extra privileges beyond what is mentioned in app manifest. See What permissions are granted to an app with device administration privileges?

Permissions are classified as normal, signature and dangerous.
See permission overview for more details. Note that these keep changing with Android versions. Create shortcuts for instance is a normal permission

More important than this classification is to know why those permissions are needed by the app. Last four mentioned by you are required by the app to be a lock screen app. As for the first three, I don't  know why they are required and it's best to ask the developer (note that reasons are not given in the app description). If you aren't satisfied with the reply don't install or install and block access using a firewall. 

I am not implying developer here is posing a risk for you but  you should know why it is required - as you care and therefore are asking. For example, here is another screen lock app that doesn't need receive data from internet