Why would Component be missing from trigger conditions?

What did you define as the alert object for the alert? It's further up on that view but not in your screenshot.

It's set on node by default... what should it be set on to see component as a trigger option? 

Any articles on it?  

Most likely Application or Component - you can look at a few of the out of the box alert templates for some examples of the configurations.

Create an alert for monitored components in SAM (solarwinds.com)

   i don't have either options listed. 

Here is a little 'gotcha' you may run into with alerting. Make sure you are using either Application or Component. You can't always mix and match them in the alert conditions. If you are setting up a Component alert make sure you choose Component. At the Application level some of the logic is 'all of the components of the application' 

I was assuming that you have already set up SAM templates to monitor the services or applications? Do you have SAM and have you configured any Service or Application monitoring templates?

No, I'm new to this company and solarwinds was already setup. They haven't used it for restarting services or applications.  I also don't see any matching templates for it.