How to run XnView MP Version 0.83 on Xubuntu 16.10?

I guess you are talking about XnViewMP 0.83 and not XnView 1.73. This is how I got 64-bit version of XnViewMP 0.83 working after downloading it from the link you have provided (you can just copy and paste these commands after you have installed the .deb package):

cd /tmp/
wget http://mirrors.kernel.org/ubuntu/pool/main/g/gstreamer0.10/libgstreamer0.10-0_0.10.36-1ubuntu1_amd64.deb http://mirrors.kernel.org/ubuntu/pool/main/g/gst-plugins-base0.10/libgstreamer-plugins-base0.10-0_0.10.36-1_amd64.deb
dpkg -x libgstreamer0.10-0_0.10.36-1ubuntu1_amd64.deb libgstreamer0.10-0_0.10.36-1ubuntu1_amd64
dpkg -x libgstreamer-plugins-base0.10-0_0.10.36-1_amd64.deb libgstreamer-plugins-base0.10-0_0.10.36-1_amd64
sudo cp -av libgstreamer0.10-0_0.10.36-1ubuntu1_amd64/usr/lib/x86_64-linux-gnu/* libgstreamer-plugins-base0.10-0_0.10.36-1_amd64/usr/lib/x86_64-linux-gnu/* /opt/XnView/lib/
rm -rf libgstreamer-plugins-base0.10-0_0.10.36-1_amd64* libgstreamer0.10-0_0.10.36-1ubuntu1_amd64*

Above commands will download and put all needed libraries to XnViewMP lib folder.

I think this can be considered a bug, since XnViewMP shouldn't require libraries which do not exist anymore.

You can get XnView from the GetDeb repositories, which provide the xnviewmp package in version 0.83-1~getdeb1 at the time of writing, including a build for 16.10.

To set up the GetDeb Apps repository as software source for your 16.10 (Yakkety) system, run these two commands:

sudo tee /etc/apt/sources.list.d/getdeb-apps.list <<< 'deb http://archive.getdeb.net/ubuntu yakkety-getdeb apps'
wget -q -O- http://archive.getdeb.net/getdeb-archive.key | sudo apt-key add -

Then update your package lists:

sudo apt update

Now you can install XnView by simply running:

sudo apt install xnviewmp