I had the same issue. It has to do with the registered assemblies in the videoplayerpage.aspx form referencing Version 16 assemblies of Microsoft.SharePoint. As far as I can tell these versions are only used in Office 365 (as of today's post). I found this out when I tried migrating another page layout from an office 365 site to an on-prem site.
Anyways, I found a workaround to get the page to at least display and play the video. It's not the best solution because you'd have to update every page and library manually. Or you could write a ps script to copy the updated file to each media library.
Also, I'm not sure if in a future update Microsoft would overwrite these files. So just be aware.
Open SharePoint designer and navigate to your library. Then navigate to Forms>Video>videoplayerpage.aspx. Edit in advanced mode and replace all the Register tags with this:
<%@ Register TagPrefix="WpNs2" Namespace="Microsoft.Office.Server.WebControls" Assembly="Microsoft.Office.DocumentManagement, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c"%>
<%@ Register TagPrefix="WpNs1" Namespace="Microsoft.SharePoint.Publishing.WebControls" Assembly="Microsoft.SharePoint.Publishing, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c"%>
<%@ Register TagPrefix="WpNs0" Namespace="Microsoft.SharePoint.WebPartPages" Assembly="Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Page language="C#" MasterPageFile="~masterurl/default.master" inherits="Microsoft.SharePoint.WebPartPages.WebPartPage,Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" meta:webpartpageexpansion="full" meta:progid="SharePoint.WebPartPage.Document" %>
<%@ Register Tagprefix="SharePoint" Namespace="Microsoft.SharePoint.WebControls" Assembly="Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %> <%@ Register Tagprefix="Utilities" Namespace="Microsoft.SharePoint.Utilities" Assembly="Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %> <%@ Import Namespace="Microsoft.SharePoint" %> <%@ Assembly Name="Microsoft.Web.CommandUI, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="WebPartPages" Namespace="Microsoft.SharePoint.WebPartPages" Assembly="Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="OfficeServer" Namespace="Microsoft.Office.Server.WebControls" Assembly="Microsoft.Office.DocumentManagement, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="SharePointWebControls" Namespace="Microsoft.SharePoint.WebControls" Assembly="Microsoft.SharePoint, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="PublishingWebControls" Namespace="Microsoft.SharePoint.Publishing.WebControls" Assembly="Microsoft.SharePoint.Publishing, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="SharePointPortalWebControls" Namespace="Microsoft.SharePoint.Portal.WebControls" Assembly="Microsoft.SharePoint.Portal, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>
<%@ Register Tagprefix="SharePointTaxonomy" Namespace="Microsoft.SharePoint.Taxonomy" Assembly="Microsoft.SharePoint.Taxonomy, Version=15.0.0.0, Culture=neutral, PublicKeyToken=71e9bce111e9429c" %>