If the main goal is redirect to the edit form - here the code of the customer_listing.xml
file which should work in your custom module (I have tested it locally and it works fine for me):
<?xml version="1.0" encoding="UTF-8"?>
<listing xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
<columns name="customer_columns" class="Magento\Customer\Ui\Component\Listing\Columns">
<settings>
<childDefaults>
<param name="fieldAction" xsi:type="array">
<item name="provider" xsi:type="string">customer_listing.customer_listing.customer_columns.actions</item>
<item name="target" xsi:type="string">applyAction</item>
<item name="params" xsi:type="array">
<item name="0" xsi:type="string">edit</item>
<item name="1" xsi:type="string">${ $.$data.rowIndex }</item>
</item>
</param>
</childDefaults>
</settings>
</columns>
</listing>
PS: Tested on Magento CE 2.2.1
Update
Here the version for the Magento < 2.2.x :
<?xml version="1.0" encoding="UTF-8"?>
<listing xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
<columns name="customer_columns" class="Magento\Customer\Ui\Component\Listing\Columns">
<argument name="data" xsi:type="array">
<item name="config" xsi:type="array">
<item name="childDefaults" xsi:type="array">
<item name="fieldAction" xsi:type="array">
<item name="provider" xsi:type="string">customer_listing.customer_listing.customer_columns.actions</item>
<item name="target" xsi:type="string">applyAction</item>
<item name="params" xsi:type="array">
<item name="0" xsi:type="string">edit</item>
<item name="1" xsi:type="boolean">${ $.$data.rowIndex }</item>
</item>
</item>
</item>
</item>
</argument>
</columns>
</listing>
Edit:
How to override :
Since a lot of people in comments were asking how to override..
you need to override the customer_index_index.xml
in this customer_listing is referenced.