I just went though my own struggles getting MATWorX 13 re-installed on a Windows 10 laptop, but the issue looks the same as you're having on Windows 11. I was getting the "Failed to get application information value" error as soon as I would click through the first few prompts from the Installer. Yes, I could have just bailed and used an old laptop or a virtual machine, but that's no fun. After digging through the TrustedInstaller code, the fix for that particular issue was to add two Registry strings that the installer was looking for (which were missing on my machine):
\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion
\HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows NT\CurrentVersion
Using regedit, I added String Values in both of those Keys with Value Name "RegisteredOrganization" and kept Value Data empty.
Once I did that, the program installed normally. But I still had a few issues: 1) the program would throw an "Unexpected error; quitting" alert when I tried to open it, 2) it would give a "System Fatal Notice" that "Object variable or With block variable not set [91]", and/or 3) it would give a notice saying COMCTL32.OCX or COMDLG32.OCX were missing or not registered correctly. The fixes for those those issues were:
1) As belvedere mentioned, always run the program(s) in Compatibility Mode for Windows XP SP2, and As Administrator if needed. That fixed the first two problems for me.
2) I copied the COMCTL32.OCX and COMDLG32.OCX files from a working machine and dropped them into C:\Windows\SysWOW64 (you could make a copy of or rename the files if they exist already). I then re-registered the files by running the following in an elevated Command Prompt:
C:\Windows\SysWOW64\regsvr32 C:\Windows\SysWOW64\comctl32.ocx
C:\Windows\SysWOW64\regsvr32 C:\Windows\SysWOW64\comdlg32.ocx
After that, the program opened and functioned normally for me (so far). I can't guarantee this will all work on Windows 11, but hope it helps! Also let me know if you want/need a copy of those two Visual Basic files.