Windows 10 won't run games with SafeDisc or Securom DRM

Or to re-word this in plain English: DRM was hooking Win32 APIs in an unauthorised way, Microsoft is utilising both improved compiler tech' as well as new coding techniques to detect/fight tampering. The goal is to stop malware from hooking Win32 to steal user information or otherwise perform exploits which might raise their access level (e.g. out of a sandbox). If Microsoft wanted to avoid breaking this DRM they would literally have to make their stuff less secure and ignore modern technologies which are designed to prevent/make it harder to do exactly this.

Not only has Microsoft made the right decision, but it was really the only decision they could make. They cannot just ignore new security technology because some DRM was written to exploit Windows back two versions ago. It sucks that users get caught in the middle, but DRM always kind of did that by its nature (legit users get caught between the publisher and pirates).

The short is: DRM is malware, Microsoft secured Windows against malware, DRM broke.

This choice is long-term good if it reduces the use of DRM, but it's pretty user-hostile right now.

No chance of running in a "Windows 7 compatibility" mode that allows the DRM to keep working?

I'm pretty sure Windows 7 compatibility mode just makes it so that when a program asks "What version of Windows am I running on?" the system will lie and say "Windows 7." The rest of the compatibility comes from shims written to patch popular and broken applications that incorrectly used Windows APIs in incorrect ways or expected different results from specific calls. Patching broken DRM is beyond what the backwards compatibility can do. SecureROM for instance had a low-level DLL in system32 and games that were "secured" with that DRM used it to take advantage of the system. I read this as that Microsoft isn't providing a way to install that DLL anymore and it would potentially open up an attack vector if they allowed it.