batch convert directories

Photoshop CS4 has File>Scripts>Image Processor that has a check box to keep the Folder Structure.

You'd just have to test it to see if it works in your case.

Are you simply mirroring the screen on your computer to display your photos on the TV or creating an actual slideshow?  If you create a slideshow, you can output the video for playing on the TV, using an HD resolution.  Your original TIFF files will be converted to the lower resolution for viewing on your TV. 

If you have a 4k TV, you could use Premiere Elements to create a 4k video from your TIFF files for viewing on the TV at the higher resolution.  (If your TV is 8k and you want to display at that resolution, you will have to find other authoring software.  However, I don't think you will find any noticeable upgrade in quality, using an 8k slideshow.)

I want to batch convert thousands of TIF files to JPG on a network drive in a directory with over 100 subdirectories to a different network drive.  Will the batch convert process create the same directory/subdirectory steructure on the new drive? 

By @Charles29078907ctdn

Is it a question for Photoshop Elements or Photoshop?

You are in the Photoshop Elements forum, and I don't know myself any possible solution with the 'process multiple files' command. That will scan the selected folder and its subfolders, but theconverted result will land on a single destination folder.

Exporting as new files with the organizer would do about the same.

That may be possible with Bridge, which is free to install from the Desktop Creative Cloud free app.

I seem to remember that I have done something similar with free external batch tools like Faststone, Irfanview, XnviewMP... But I don't use network drives.