No, a running program can't be uninstalled, so it's impossible a program uninstalls itself.
The "legit" site you mention only offers me a login screen, so is no help at all.
And the logs only show you run their chat program from your appdata\roaming folder.
However, they are the only ones that can help you with your issue. So either try again or accept it's a program that isn't suitable for you.
Here's the legit site for this software: https://streamlabs.com/dashboard#/streamlabels Link takes to login screen cause account required for access. If someone here who also has access to this fine page & knows about this problem then let me know
Wondering why my legit & safe Streamlabels software uninstalled itself few days ago. it wasn't open when it vanished. Today when i downloaded new installer and started to install it then it got stuck to about 25% and nothing happened in over 5mins. Tried twice and same thing So moments ago i did a scan with HijackThis software & marked some log files that had (file missing). Then clicked "Analyze this" & i got a window popup to sourceforge/requests page.
There was a note that it's crowded and they're not doing anything. They had added few sites that could help and one of them was cnet.com forums. I'll add the log file from HijackThis prog. I'm using Bitdefender Free Antivir. I don't think that it would uninstall softwares on it's own & i did a scan with malwarebytes some days ago and found no bugs. Same with SuperAntiSpyware software (if that was the name can't recall now). Though maybe i could do the scan again with SuperAntiSpyware now that this self uninstalling happened.