I found a way to make Steam Link working on Big Sur.

You need to disable SIP in RecoveryOS to install Gamepad and Audio kexts. Reboot every time when macOS asking for it and you are done:)

1. Reboot your Apple computer and press Cmd+R when in starting
2. Login, enter password if asked, etc.
3. Press Utilities -> Terminal and type csrutil disable and press Enter
4. Type reboot and press Enter
5. Log in into normal macOS and try to connect to Steam Link
6. You will be asked to install Gamepad kexts as usual BUT now in Security & Privacy settings you'll see this Allow button
7. Reboot as macOS asking
8. Try to connect to Steam Link
9. Repeat from p.6 for Audio kext

Enjoy.


NOTE:
In my experience with SIP, old macbooks with Big Sur installed haven't Recovery OS (Cmd+R on laptop starting) and it will start to download it from the Internet.

DON'T DOWNLOAD IT!
csrutil was updated in Big Sur and if you'll disable it with older Recovery OS, it will be broken. You need macOS Big Sur Install stick/another media to disable SIP correctly

To use Steam Link without this workaround, Steam devs team needs to recompile this kexts with newer cert/permissions (dunno exactly) for Big Sur. So only way to avoid workaround -- waiting for it