Yeah you need a k8s cluster, but even a simple kind dev cluster that you spin up in 30 seconds with one command on your laptop will work.
I like it a lot because it enforces very little structure on you and doesn't reinvent everything. Stuff like storage (either ephermeral or existing volumes), secrets, configuration, etc. are already modeled and supported by Kubernetes and tekton can use all of that natively. And since it's all k8s native stuff you have all of the power of k8s, like its entire API for manipulating and managing execution, exposing services, etc. There is very little cognitive overhead or new things to learn once you know k8s.
If you're really averse to k8s though, check out drone. It has a local execution mode that is similar and just runs whatever pipeline commands you want in docker containers. https://github.com/drone/drone Batect is another even more minimal tool that's effectively just a docker-based workflow system: https://github.com/batect/batect