From the rules we can see that the Fabricator General is in the game (good for me as I love Mechanicum/Adeptus Mechanicus). However, he is a loyalist hero, not a Chaos one.

*SPOILER START*

But as we know from the novel "Mechanicum", the Fabricator General was Kelbor-Hal back then and he sided with Chaos attacking the loyalists of the Mechanicum on Mars prior to the Battle for Terra. Ok, the HH novel cycle hasn't reached the Battle for Tera yet. However, the Collected Visions book doesn't mention anything like that. And I don't think that the loyalists quickly elected a new Fabricator General (also if they did, where is Kelbor-Hal during the battle)?

*SPOILER END*

Then of course they got some names wrong, as Custodes, Arbites and Mechanicum are not yet "Adeptus", that happened after the Horus Heresy.

In the original game and backstory, Kane replaced the Fabricator General as the Loyalist leader of the Mechanicum (General Kane was a counter in the orig. game) when the original (Kelbor-Hal) joined with Horus. So in a sense, he is the Loyalist Fabricator General.