If I say "source is available and you can make modifications, but only if you have red hair and live in Brazil", is this open source?
It's not as specific as the OSI definition of course, and it doesn't say anything about redistribution and such, but that's okay and it doesn't really need to be IMO. Some vagueness is okay, and even with the OSI definition there is a huge difference between something like MIT and AGPL, both of whom are "open source".
People talk about permissive and copyleft licenses when the distinction matters. Covering both doesn't make open source vague.
Alternative definitions restrict the freedom to run the software at all frequently. Never mind modifying it.
The only thing you are saying is that other people tried to use "open source" for something else and completely and utterly failed to convince people. Thus, today "open source" means what it means.