For the curious, an automatic centre punch is the basis of whatever he used - https://www.amazon.co.uk/Starrett-18AA-Automatic-Centre-Adjustable/dp/B0006J4Q5U
Besides a Magpul Armorer's Wrench and a Punch Set (there are cheaper versions of each but these are what I own), I'd add a few tools to make this much easier and add addendums to a few of these. Punch set: you're gonna at least need the 1/16th and 3/32 punches if you're buying individually. I'd get 2 of each as they can bend pretty easily. Also a hammer, preferably rubber/brass.
Auto punch for staking castle nut, not 100% necessary but makes staking much easier.
Pivot roll pin tool makes insertion of roll pins much easier, saves your fingers a bit.
Some electrical tape can be used to cover parts you don't want to scratch when assembling. I personally don't care (more scratches imo makes it look like it actually gets used).
Also, Adjustable Mini Pliers Wrench that I use for inserting some of the roll pins. Wrap the end in electrical tape and press. Easier than hammering away at some of them. The trigger guard tool that comes with the wheeler punch set can replace this but I've used it for tons of shit so why not.
Here are some commonly used and often overlooked tools that I use every day and have multiples of in case one goes missing
small flashlight: https://smile.amazon.com/gp/product/B008X2QMKY/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
Edge Technology Speedy tool height setter: (This thing is badass and super quick for manual lathe setup) http://www.edgetechnologyproducts.com/speedy-lathe-gage/