InfoPath is not included in Office 2016

Yes,
InfoPath 2013 is the last release of the desktop client, and InfoPath Forms Services in SharePoint Server 2013 is the last release of InfoPath Forms Services. The InfoPath Forms Services technology within Office 365 will be maintained and it will function until further notice.

We also want to remind you that the InfoPath 2013 desktop client and InfoPath Forms Services for SharePoint Server 2013 will continue to be supported through 2023 2026 as part of our Online Services Support Lifecycle Policy

InfoPath Forms Services will be included in the next on-premises release of SharePoint Server 2016, as well as being fully supported in Office 365 until further notice. Customers will be able to confidently migrate to SharePoint Server 2016 knowing that their InfoPath forms
will continue to work in their on-premises environments, as well as in Office 365.  

InfoPath frequently asked questions

1. Will Microsoft be shipping another version of InfoPath?

No, there will not be another version of the InfoPath desktop client or InfoPath
Forms Services. We are focusing all of our investments on new intelligent,
integrated forms experiences across Office technology.

2. How long will InfoPath be supported?

  • The InfoPath 2013 client will be supported through 2023 2026.
  • InfoPath Forms Services in Office 365 will be supported until further notice.

For more information on InfoPath Forms Services support in Office 365, please review our Online Services Support Lifecycle Policy

3. How to work with Infopath when Office 2016 installed.

Download and install Infopath O365 subscription at https://www.microsoft.com/en-us/download/details.aspx?id=48734 

4.How to upgrade office 2013 to office 2016

We generally will always recommend removing the previous app first, then installing the next version cleanly and as you pointed out, it is best to start with the oldest and move to the newer versions of Office products.  If the majority of the environment just has Office 2013, and needs Office 2016, I would recommend using Offscrub to remove 2013, and then move to 2016 cleanly.
Here is a blog https://blogs.technet.com/b/odsupport/archive/2015/12/01/supported-scenarios-of-multiple-office-products.aspx

on moving from 2010 to 2013, but the principles are the same with moving to 2016 as well.

It does get tricky when we need to have mixed versions. If you have a large number of clients that do need to keep InfoPath 2013, then it would be best to not do an uninstall of 2013 first, before upgrading to 2016. Just let Office 2016 uninstall 2013. As you saw, InfoPath 2013 will stay behind as there is no direct upgrade in 2016. So you will be left with Office 2016 and InfoPath 2013. And if you have any machines with Visio/Project 2010, they will be unaffected by this as well. There are potential issues doing it this way most notably, if a user’s 2013 is corrupted, the migration will likely fail. But for the most part, this should be a smooth transition overall.

We would recommend against installing 2016, then if everything looks good, uninstall 2013. That seems like a safe approach as the user is never without Office, but it will require a repair or a configuration of 2016 after the 2013 removal

Reference:

https://blogs.office.com/2016/01/20/sharepoint-server-2016-and-project-server-2016-release-candidate-available/

https://support.office.com/en-US/article/Install-and-use-multiple-versions-of-Office-on-the-same-PC-6ebb44ce-18a3-43f9-a187-b78c513788bf

https://support.office.com/en-us/article/Install-and-use-different-versions-of-Office-on-the-same-PC-6ebb44ce-18a3-43f9-a187-b78c513788bf?ui=en-US&rs=en-US&ad=US

Published By: Neelesh Singh Rai