What you're looking for is called Mandatory Access Control, or MAC. Android enables it by default and it is tightly integrated into the userland APIs, but the technologies that lie at base of the MAC in Android (i.e., SELinux) are part of the default Linux kernel. Additionally, there exists another framework for MAC called AppArmor, which android does not use but which has similar features.
Configuring SELinux or AppArmor is not for the faint of heart. However, many distributions ship with default SELinux and/or AppArmor policies that you can use. For instance, Ubuntu ships with AppArmor enabled by default, and RHEL/CentOS ship with a few SELinux rule sets that you can choose from, with the least restrictive one of the set being enabled by default. Debian, too, has an SELinux rule set that it ships with, but it is not enabled by default, and it is not as well tested with SELinux enabled.
Most of the distributions that ship with MAC enabled don't have a very restrictive set of rules; after all, if it gets in the way too much, people will just disable it, and then you don't reap the benefits. However, it's certainly possible to enable a more restrictive set of rules -- it just means you may need to debug things a bit more, as most applications on the Linux desktop are not tested with MAC enabled.
One feature of some SELinux rule sets is the "SELinux sandbox". If you use that, applications that run inside it will have very few permissions. This can be useful to test an application without risk of it misbehaving and eating your files. For more information on that, you can read https://www.linux.com/learn/run-applications-secure-sandboxes-selinux.