Failed to reproduce your issue,you could follow my working steps as below:
1.Import repository,I used the git url from this document:https://github.com/MicrosoftDocs/pipelines-javascript

2.Create Build Pipeline.

3.Run the Build process.

4.Release the project and choose Nodejs Web APP.

5.Choosing the azure web app service in your subscription.

6.Navigate to your project url.

7.My files in the /wwwroot directory.

And web.config
file as below:
<?xml version="1.0" encoding="utf-8"?>
<!--
This configuration file is required if iisnode is used to run node processes behind
IIS or IIS Express. For more information, visit:
https://github.com/tjanczuk/iisnode/blob/master/src/samples/configuration/web.config
-->
<configuration>
<system.webServer>
<!-- Visit http://blogs.msdn.com/b/windowsazure/archive/2013/11/14/introduction-to-websockets-on-windows-azure-web-sites.aspx for more information on WebSocket support -->
<webSocket enabled="false" />
<handlers>
<!-- Indicates that the server.js file is a node.js site to be handled by the iisnode module -->
<add name="iisnode" path="server.js" verb="*" modules="iisnode"/>
</handlers>
<rewrite>
<rules>
<!-- Do not interfere with requests for node-inspector debugging -->
<rule name="NodeInspector" patternSyntax="ECMAScript" stopProcessing="true">
<match url="^server.js\/debug[\/]?" />
</rule>
<!-- First we consider whether the incoming URL matches a physical file in the /public folder -->
<rule name="StaticContent">
<action type="Rewrite" url="public{REQUEST_URI}"/>
</rule>
<!-- All other URLs are mapped to the node.js site entry point -->
<rule name="DynamicContent">
<conditions>
<add input="{REQUEST_FILENAME}" matchType="IsFile" negate="True"/>
</conditions>
<action type="Rewrite" url="server.js"/>
</rule>
</rules>
</rewrite>
<!-- 'bin' directory has no special meaning in node.js and apps can be placed in it -->
<security>
<requestFiltering>
<hiddenSegments>
<remove segment="bin"/>
</hiddenSegments>
</requestFiltering>
</security>
<!-- Make sure error responses are left untouched -->
<httpErrors existingResponse="PassThrough" />
<!--
You can control how Node is hosted within IIS using the following options:
* watchedFiles: semi-colon separated list of files that will be watched for changes to restart the server
* node_env: will be propagated to node as NODE_ENV environment variable
* debuggingEnabled - controls whether the built-in debugger is enabled
See https://github.com/tjanczuk/iisnode/blob/master/src/samples/configuration/web.config for a full list of options
-->
<!--<iisnode watchedFiles="web.config;*.js"/>-->
</system.webServer>
</configuration>
You could check any differences between your steps and mine.Any concern,please let me know.