Using Deno you can run WebAssembly modules on a server because the Deno wasi module provides an implementation of WASI, the WebAssembly system interface. Using Deno is just one way of running wasm modules on a server. You could choose between many other implementations of WASI, like the wasi module in Node.js, wasmtime, lucet, wasmer, etc.
Code [running] outside of a browser needs a way to talk to the system — a system interface.
As for your security concerns, keep in mind that your WebAssembly code runs in a sandboxed environment. It's not your host system that executes directly the code in your wasm module. It's the wasm runtime — that implements the WASI interface — that runs it. And as far as I know the only way for your code to produce side effects (e.g. perform a HTTP call, access files) is to go through appropriate APIs defined by WASI.