On windows 10; I get an error "the 3D rendering engine could not be initialized". Is there something I can do?

Yes ! On game application in folder of the game,select de game executable... properties... at compatibility.. settings reduce color mode checkbox... put it 8-bit for the first game... and i think on Syberia 2 works on 16- bit noproblem..
If the game ask you for Direct play... write in the windows taskbar... windows feature and look for directplay and enable it.... windows will take some time to make the feature available.. Windows 10 :)

DirectPlay is at Legacy components folder in Windows Feature :)... if needed, activate it... no need for downloads.. windows 10 has this feature... but is turned off :)

Be well!!

For me, the solution was to right-click on game.exe (in the Syberia installation folder) and then click Properties.

Then, under the Compatibility tab, check the box that says "Run in 640 x 480 screen resolution". Then press OK and run the game.

No other options in the Compatibility tab need to be changed, and when I did change other settings along with checking the box that says "Run in 640 x 480 screen resolution", the game still wouldn't launch for me.

So, I recommend checking that "Run in 640 x 480 screen resolution" box only, and then running the game.

I've managed to start the game by following this (steamcommunity.com/app/46500/discussions/0/358415206083712430/) guide. (Duplicating below)
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For all of you who tried to run Syberia 1 and 2 on modern operating sysystem like Windows 7/8/10 and encountered problem like 3D Accellerator Error, Glich, problem to run the game i founded a simple solution without use compatible mode or clor reduction.

i resolved in a very simple way using the program "dgVoodoo 2", a program created to emulate old graphic card and libraries.

Research the program with google and download the last version (you will download a rar archive)

In the rar you can find an exe file and two folders claeed "Glide" and "MS"
After the download copy the .exe file and the content of the libraries file (MS Folder) in the same directory where you installed Syberia 1 or 2.
Select the option Fullscreen and the voice "Streched" to have the full screen filled.
To the voice "Output API" select "Best Aviable one"
To the voice "Adapter to use" select "All of them"

Go to the tab DirectX and tho the voice "Videocard " select "dgVoodoo Virtual 3D Accellerator Card"

Click on the Botton Apply and after on "Ok",

Close the program and run Syberia with Game.exe.

Syberia 1 and 2 should go without problems
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BUT I copied content of MS/x86/
Used dgVoodoo 2.75.1

UPDATE: If mouse is moving only in small area go to DirectX tab and set your resolution. Also might be helpful to alt+tab couple of times to apply resolution

Also no compatibility options were checked