I get the following error:
Installation file not found:
administrator/components/com_installer/mambot/plugin_jw_allvideos/

What am I doing wrong??

I uploaded the plugin_jw_allvideos folder to the mambot folder. It contains 8 files.

This is how you should install it.

Go to your Joomla control panel > Installers > Mambot > Browse > find the mambot you downloaded and upload.
Then go to Joomala CP > Mambots > find AllVideos Plugin > Click the red x to publish it. Now it's live.
Before or after (it don't matter), click on the AllVideo Plugin name. Inside you will find a very complete and easy to understand instructions on how to use it.

I did that. It won't work. I've got these files:

bullet.png
gz_eolas_fix.js
jw_allvideos_player.swf
logo.gif
star.png
tab_bg.png
tabs.css
tabs.js

I've never tried uploading the mambot directly to the ftp. So I took a look at where the mambot installed on my ftp and my path is completely different from yours. /public_html/mambots/content/plugin_jw_allvideos/

I can't get my server to let me upload the .zip file, so I manually upload via ftp and install. But that's not possible :|

Did you at least try uploading it to the correct folder, the one I gave you? The folder you indicated in you first first post is obviously the wrong one.

I have to install it. And the installer says there is no install file.

Uploading it to the folder you told me to, does nothing. There still is no installment file.  :(

I don't know anything about installers, never heard of them. I have only installed a couple hundred components, modules and mambots using the Joomla Control Panel. I really don't know how to do it any other way. I'm pretty new at this stuff. 

You should upload these three items found in your AllVideo Rar/Zip file to /public_html/mambots/contents/
plugin_jw_allvideos (folder)
plugin_jw_allvideos.php
plugin_jw_allvideos.xml

Oh my GOD, I feel so dumb! I had overlooked those two files and just uploaded the rest. Ahem...

Is it possible to use the video plugin on the fireboard? If I want people to be able to post streaming videos from google, youtube and so on?

You will have to see if somebody there has come up with something. I use SMF with which I can insert youtube videos. I'm sure Fireboard will have something soon for that if not already.