I have the same problem, but I'm, able run it manually from a terminal:
cd /Volumes/ums-7.2.1-distribution/Universal\ Media\ Server.app/Contents/MacOS/
./UMS &
it display a lot of debugging info, but it works since several older versions
INFO 21:26:09.423 [main] Starting Universal Media Server 7 ...
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- Thu Aug 16, 2018 2:33 pm
- Forum: Help and Support
- Topic: UMS 7.1.0 won't launch in High Sierra
- Replies: 5
- Views: 17278