The script is doing what you have written -- figure out the way to a particular point (where the target was when it started walking), then walk there.

Since that takes time, though, the original path isn't the path you want to keep following by the time you get there.

The simplest solution is to re-evaluate the path every few seconds and instead follow that path

First, just the following-a-path. You don't need to spawn your code like you are now.

This will look for path, a list of Vector3s, and repeatedly walk to the first one, removing it.

local path = {} -- a list of Vector3s

while wait() do
	if #path > 0 then
		-- There's at least one step on the path
		local go = table.remove(path, 1) -- Get the first step of the path
		humanoid:MoveTo(go)
		humanoid.MoveToFinished:wait()
	end
end

This loops looks just at whatever the first element of path is -- but it's OK with path changing entirely. To make it follow more accurately, just swap out path:

local players = game.Players:GetPlayers()
local target = player[math.random(#players)]
while wait(1) do
	-- Once a second, update the path (not too often -- this is slow)
	local from = script.Parent.Torso
	local to = target.Character.Torso
	path = PathfindingService:ComputeSmoothPathAsync(from, to, 500)
		:GetPointCoordinates()
end

Just spawn one of these two so that they can work together.

Problem

You said the humanoid would sometimes take a step back and then continue on its way.

I'm guessing that's because it has to "round" its position to the grid, which might be slightly behind it.

Assuming that you don't have extremely tight corners, the solution could be to just remove the first step from the path:

	path = PathfindingService:ComputeSmoothPathAsync(from, to, 500)
		:GetPointCoordinates()
	table.remove(path, 1)

I'm not exactly sure how the output of ComputeSmoothPathAsync works. It might be necessary to add a check to only remove the first point from path if that first point is very close (< 4 studs) to the player.