I hope it is ok and permitted to post the replies from Costumer Support - to help possibly other players:
Thank you for contacting 2K Support.
I am sorry that you are still having issues with the combat animations in Beyond Earth.
It appears that you are receiving core Windows Operating System .dll file crashes. When corrupted, these tend to cause issues across a number of applications.
As with any Windows corruption, it may be a good idea to start with a virus scanner. File corruption can be caused by a variety of factors, most completely unrelated to malware, but it is always a good idea to run a scan if you see these types of errors.
Once the virus scan is complete, we are going to use the sfc /scannow tool, to check for system corruption, and hopefully repair any damaged files.
The sfc /scannow command (System File Checker) scans the integrity of all protected Windows 7 system files and replaces incorrect corrupted, changed/modified, or damaged versions with the correct versions if possible.
*Warning*
*Be aware that if you have modified your system files as in theming explorer/system files, running sfc /scannow will revert the system files such as explorer.exe back to it's default state. Make the appropriate backups of your system files that you have modified for theming if you wish to save them before running sfc /scannow.*
To Run the SFC /SCANNOW Command in Windows 7:
1) Navigate to the Start Menu->All Programs->Accessories==> Then right-click on Command Prompt and select Run as Administrator
2) To Scan and Repair System Files NOTE: Scans the integrity of all protected system files and repairs the system files if needed. Please see above.
3) In the elevated command prompt, type the following and press Enter: sfc /scannow
NOTE: This may take a little bit to finish.
4) When the scan is complete, hopefully all files will pass, and it will say \Windows Resource Protection did not find any integrity violations.
**If SFC could not fix something, then run the command again to see if it may be able to the next time. Sometimes it may take running the sfc /scannow command 3 or more times to completely fix everything that it's able to.
**If not, then you can attempt to run a System Restore using a restore point dated before the bad file occured to fix it. You may need to repeat doing a System Restore until you find a older restore point that may work.
5) When done, close the elevated command prompt.
If none of these resolves the issue, it may be worth creating a new Windows user log-in with administrative privileges, and try running the game from there, and see if that resolves your issue.
If you have any further questions please do not hesitate to ask.
Go forth and conquer the world!
Jason L.
2K Support