Do I have to buy a Mac Mini to install this

No. OpenClaw runs on macOS or Linux (Windows via WSL2). A Mac mini is optional - some people buy one as an always‑on host, but a small VPS, home server, or Raspberry Pi‑class box works too.
You only need a Mac for macOS‑only tools. For iMessage, you can keep the Gateway on Linux and run imsg on any Mac over SSH by pointing channels.imessage.cliPath at an SSH wrapper. If you want other macOS‑only tools, run the Gateway on a Mac or pair a macOS node.
Docs: iMessage, Nodes, Mac remote mode.