You can only load triggers from an edition that supports Apex.
If you want to delete triggers from a live org, you don't need to involve Eclipse. I typically use the Developer Workbench and a destructiveChanges.xml file.
You have to actually include the triggers in your package.xml
file.
<?xml version="1.0" encoding="UTF-8"?>
<Package xmlns="http://soap.sforce.com/2006/04/metadata">
<types>
<members>*</members>
<name>ApexTrigger</name>
</types>
<version>39.0</version>
</Package>
My typical package includes these types:
<?xml version="1.0" encoding="UTF-8"?>
<Package xmlns="http://soap.sforce.com/2006/04/metadata">
<types>
<members>*</members>
<name>ApexClass</name>
</types>
<types>
<members>*</members>
<name>ApexComponent</name>
</types>
<types>
<members>*</members>
<name>ApexPage</name>
</types>
<types>
<members>*</members>
<name>ApexTrigger</name>
</types>
<types>
<members>*</members>
<name>CustomLabel</name>
</types>
<types>
<members>*</members>
<name>StaticResource</name>
</types>
<version>39.0</version>
</Package>
package.xml
.