Try connecting the OTG adapter to the camera.
This is what I used to do.
As the camera is self powered, it doesn't draw power from the USB host device.

I used to use my SGT 7"(Android 4.4) with my D300 way back.
Was an OK system, loaded a few apps to view images, loaded something(can't recall now) to view NEF files directly.
Screen wasn't too nice, so the plan to possibly edit some images as time allowed went down like a lead balloon!
Bit it was handy to be able to review some images on a larger screen when time allowed.
More importantly was the backup.
I used to backup to a portable HDD.

In saying all this tho, my OTG cable/device was slightly different to what I just scrolled up and saw in your pic.
The Galaxy Tab of old had this totally silly 'Apple like' connector(not straight USB type port), and the OTG adapter I found has car reading ports on it, and a USB host port(like you PC does .. a USB A plug)
SO I could use it as a reader, or as a USB host converter(Android does USB host). Had to flip a small switch between car slots and USB port for it to recognise the camera .. but my CF card reader was the camera.
Never failed.

With the CF card issue:
try some stuff ...

1/. format the CF card via Windows, use exfat or fat32. see if this recognises the CF card.
2/. do you have any SD cards. D810 series has 1CF and 1 SD card slot. If you have any SD cards, take some images saved on the SD card using the camera, see if this works.(this is assuming you're shooting NEF, not jpg.
3/. a couple of test shots using jpg mode on the D810 on the CF cards. Does the tablet see the jpgs on the CF card now?
4/. have you loaded a NEF codec on the tablet?
Basically the above relates to the ability for Android to 'see' NEF file types. Natively it doesn't, so you need an app that does, or an NEF codec(decoder) on the tablet. Just get an app that allows you to view raw files.

I know CF cards can be weird(ie do weird things).
I went from a D300 to a D800E. The CF card I used in the D300(Patriot brand) was a ripper(for the time) .. super fast, never let me down.
No way I could get the Patriot CF card to work in the D800E, even tho it worked perfectly in the D300!
I got a reasonably fast Lexar CF card for the D800E, but the Patriot CF card was faster(testing on Windows) .. just wouldn't work on the D800E.

But as above CF cards natively should work on Android, as long as they're formatted OK(ie. not NTFS). Can't remember what format Nikon use .. I think FAT32 .. which is fine on Android anyhow.

Also to note .. the host device(ie. smart phone, PC, tablet .. etc .. these are the Host devices) .. they actually don't see the card directly.
The see the card via the adapter. The adapter could be anything, just so happens that your adapter is device A from manufacturer B(ie. your card reader).
The card itself is an ATA device, like the old gen hard drives, that used the UDMA1-7 interface .. now HDDs are SATA.
So the CF card is something like a UDMA6 or 7 device .. not really a CF card.
The card reader is a UDMA(or ATA) to USB adapter. The Host 'sees' the storage device only via the adapter, so could be the card reader.
So technically speaking, you don't see the card itself, you see its file system via the interface type it uses(that UDMA/ATA/SATA/USB stuff).

I'm thinking tho, that most likely is that you have NEF files on the card, and Android can't see these.
Note when I mention the NEF(or raw) codec, I don't mean a converter as such. I mean you could convert them if you want too, but if you got an app that can convert raw files(ie. NEF) to jpg, then it can read NEF files.
As long as this app is flexible enough that you can point it to any directory/device .. then you should be able to see the files on the CF card(not so much the CF card itself)

Easy test to do for now(to gather more data) is .. connect camera to tablet via the OTG lead. See if this works first.
And have both NEF and jpg files to play with.
I reckon, as long as the card reader is fine, then if you had two images one in NEF and one in jpg, using even a simple app like Gallery, you should see the jpg file on the CF card.


One other tip, look for an app for the tablet(or phone) called X-plore. It's a file browser.
I used to use ES File Explorer, but it turned to garbage. Found X-Plore much better replacement anyhow .. so even if ES was still unbloated rubbish .. would have changed to X-Plore anyhow.
Might seem a little confusing at first .. but it's so much more intuitive once got used too.