You do not have uninstall, reinstall or install items in any specific order. You simply need to install and then select them in the appropriate place in the DAW software.

The MOXF REMOTE TOOLS will allow you to construct templates for various third party VSTi plug-ins, just do you know.
The Extensions allow Cubase to select and route audio Ports via the VST EDITOR.

"MOXF6/MOXF8 Remote Editor is a convenient tool which lets you edit/create Control Templates for the MOXF6/MOXF8 Music Synthesizer. These Control Templates let you assign the appropriate functions for your favorite VSTi to the Knobs on the MOXF6/MOXF8. While the MOXF6/MOXF8 handles up to 50 Control Templates (in a single Bank), the MOXF6/MOXF8 Remote Editor can be used to create and organize multiple Bank files, each of which contain 50 Control Templates. Data of a single Bank containing 50 Control Templates created on the MOXF6/MOXF8 Remote Editor can be transferred from the computer to the MOXF6/MOXF8 and saved to the computer as a single Bank file.

MOXF6/MOXF8 Extension is software component that enables you to use the MOXF6/MOXF8 along with Cubase series. The MOXF6/MOXF8 Remote Tools Installer installs these two software components."

It may simply be that you need reinitiate the plugins that were previously there.

Go to DEVICES > PLUGIN MANAGER

For basic setup instructions for setting up to record MIDI to Cubase please see the following:
MOXF Basic MIDI Recording

I tried going to the Devices>Plugin Manger in Cubase and saw the Yamaha Extensions in the Program plugins section. It was unchecked and when I tried to check it I got an error saying that it would not initialize. I also tried to add the MOXF6 / MOXF8 remote in the Device Setup screen and it also said that it would not initialize. I also have Cubase LE AI 7 on the same computer that came with another manufacturer's guitar pedal and it works fine but I had loaded the Remote Tools and extensions BEFORE starting version 7. The problem, it seems is that I started Cubase 8 and tried to use the Yamaha USB / ASIO before loading the remote tools. That seems to be the only variable I can see between the two. Everything else seems to work fine on version 8 except the extensions.

Here is another update on my problem with Cubase LE AI 8 and Yamaha's Remote Tools. I decided to reinstall both the Yamaha / Steinberg USB drivers and Yamaha's Remote tools. After uninstalling both, I checked in the directories (Program Files / Common Files / Steinberg and Program Files 86 / Common Files / Steinberg) to make sure that the 2 dll files ( Yamaha ASIO dll and the Extension dll file) were gone, and they were. I started Cubase 8 and checked in the Devices >Plugin Information section to see if the files were gone there, and they were. I loaded Cubase 7 and checked the same thing, same result. I then reinstalled the USB driver, and then the Remote Tools, plugged the MOXF into the USB, powered it on, loaded Cubase 8 and checked in the Devices > Device Setup to see if the remote had loaded, it did not load. I then checked in the Devices > Plugin Information section to see if the program plugins had loaded. The USB driver had loaded and was checked, but the Extensions dll had loaded but was not checked. I tried (again) to check it and got the error that it could not initialize. I then loaded Cubase 7 and tried the same thing and the remote was there and the extensions dll was checked and working. This definitely points to a problem with the Cubase version 8 and the Yamaha Remote Tools extension having some kind of a problem together. I opened a ticket with Cubase on this. It looks like I'll have to reinstall Cubase 8 at this point unless you have any better ideas.

A few things the driver is the Yamaha Steinberg USB Driver, since there are different drivers we will refer to it by its correct name in hopes that this is the driver you are referring to (there is no such thing as " the Yamaha ASIO driver" that you refer to...

It should not matter the order in which install items, as long as they are all present.
Are you running 32-bit or 64-bit, this maybe your issue?

If you have contacted Steinberg through your MySteinberg Account, please provide them with your computer vitals and the build version of Cubase AI8... and ask how to reinitialize them with the PLUGIN MANAGER.

Yes, sorry the driver I'm using is the Yamaha Steinberg USB driver version 1.9.9. I'm using Windows 7 64 bit. When I installed the driver it asked me for 64 bit or 32 bit. I installed both and the .dll files are in both the C:/program files / common files / Steinberg and C: / program files 86 / common files / Steinberg directories. I assumed that since I'm using a 64 bit Windows it would automatically select the correct dll file. Was I wrong? I have opened a ticket with Steinberg, but have not received a reply. I may have a version of Cubase LE 8 that is not an advanced integration version installed on this computer, I'm not sure. In Steinberg's licencing software it says that is Cubase LE 8, but in the help menu of Cubase 8 itself it says it is a LE AI version, not sure why the two don't match.... I received several versions of Cubase LE with different equipment that I purchased and that may be the issue as I thought I installed the one from Yamaha that came with my MOXF, but now I'm not sure. I think I trashed the disc, since you can download a copy from Steinberg. Do you know if there is a difference in the LE additions that come from Cubase? Should they all be able to use the Yamaha remote tools? Another thing, I checked again in the Cubase 8 Devices > Plug In Information > Program plugins screen and the dll file that is there for what I assume is the remote tools is showing to be in the C:/ program files / common files / Steinberg directory (the 64 bit directory).

Let us know when you hear from Steinberg.
When you installed the download that MOXF8 users are given access to, you get a download that can install AI, LE or Elements. You want to select AI.
Again, when you hear from Steinberg they can help you make the selection.

LE is the light edition that Steinberg supplies to the industry (it is the introductory version you get with many hardware purchases), it has a different feature set from the "AI" version which you only get with a purchase of a Yamaha or Steinberg piece of hardware. It has specific Yamaha Extensions (Tools) and for routing capabilities you do not get in LE. It integrates the MOXF as a VST3 plugin which will let you take advantage of advanced MIDI and Audio routing within Cubase.

When you launch this version of the Cubase installation, the first thing it will do is ask which one you wish to use, select AI.
I do not believe you will see the MOXF VST option implemented in the same way in LE.

I have the exact same problem with LE AI Elements 7 (came with the MOXF8) and LE AI Elements 9. In addition, when I run the remote editor and hit File > setup, it doesn't give me any DAW option other than "Other". Please let me know if you find a solution. I will do likewise. PS. Running on latest Windows 10 64-bit

I should add that the MOXF VSTi also doesn't show up in LE AI Elements 7 when you try to create an instrument track. However, it is there in the list of active VST plug ins.

You want to make sure you are launching Cubase AI. When you are given the choice at launch select AI.