No. As of version 34 (released in July 2019), Just Press Record no longer runs on the first generation Apple Watch. Version 34 requires iOS 12 and watchOS 5, which in turn requires a Series 1 Apple Watch or later.
For existing users who have an iPhone running iOS 12 and a first generation Apple Watch (running watchOS 4), Just Press Record will be automatically removed from their Apple Watch when version 34 is installed on their iPhone.
We have continued to support iOS 11 and watchOS 4 for 10 months since the release of iOS 12 and watchOS 5. In order to continue to develop exciting new features for Just Press Record and take advantage of Apple's latest technologies it was necessity to raise the OS requirements for this release.