It's not a prerequisite, right? Or is the orbital command itself part of many Terran builds?
It is not a prerequisite for reapers. It is part of most terran build orders, getting it on 15 supply is most common. As tzenes mentioned, it has 3 abilities. A mule calldown, which gathers minerals at 3x the rate of an SCV and can share a mineral patch with an scv, a scanner sweep that reveals the area under it (including stealth units), and a call down of extra supplies on a supply depot.
The mule is the main reason it is part of nearly every terran build. The upgrade to orbital costs 150. Mules gather at 3x the rate of SCVs. An orbital starts with enough energy for a mule and produces enough energy to continuously have one mule mining. Mules don't take pop cap and the upgrade completes in less time than 2 SCVs, let alone 3. Basically this all adds up to upgrading to an orbital usually being a better economic investment than the 3 SCVs.
They additionally work well with reaper builds as reapers are gas heavy units and take up your barracks production time, thus leaving you with extra minerals that you might as well spend on improving your economy so you can have a followup to the reaper rush.
No, an Orbital Command is not a prerequisite for Reapers (or any other unit). It is a useful add on as it provides quick minerals, scans, or depots if you're low on free SCVs.
In the builds you linked, the writer is using the Orbital Command to come back from his early economic sacrifice to get out that early reaper. As someone states in the discussion section this is actually poorly presented in the build (not to mention largely inaccurate).
Nothing requires the Orbital Command be part of a Reaper rush, but with such a "cheesy" build it is largely dependent on luck, which the author may attribute to the OC.