I have no option to download the Giant's Shadow map.

Have you tried the suggestions in the read first STICKY thread @Benjie-67?

http://answers.ea.com/t5/Technical-Issues/Can-t-play-or-patch-info/m-p/5696716#U5696716

Nothing in the sticky applies to my issue.  I had no problem updating BF1 Deluxe edition, I have restarted my PC and Repaired game.  I have no access to even attempt to download the Map. 

If you have the update you should have the map. Simply start the game and join a server running the new map.

I have tried that several times. I get the loading game line and then get:

SERVER DISCONNECTED 

the server is now running content that you don't have, look in the store for available content or make sure that all your content is installed.

When I looked in the Store, that is when I noticed after selecting Deluxe, info/description page had a Buy and $ sum listed.  When I selected Premium , the info/description page displayed owned.  As per Original post the Origin App shows that I have Deluxe and Premium.

Does the map come as a DLC (like BF4 did even for free content) ?

Well, I discovered that my contribution to my issue was that I continued to connect to the same server ( [dice] official TDM US West # 36538 every time this morning. (used the recent server option)

Tonight I tried to join a South America Dice Official server with the Giant's Shadow (GS) TDM map and it loaded OK.  I tried a USA private GS TDM map, it loaded OK and then I tried an Official US East GS TDM server and got Server Disconnected "content" message.  Joining Dice Official West and East USA Conquest  servers with GS map works OK.  SO, it appears it is only (so far) Dice Official TDM servers with GS map that do not work for me!