Note the weasel words :
In tracking the performance of the Index, the Fund attempts to replicate the Index by investing all, or substantially all, of its assets in the stocks that make
up the Index, holding each stock in approximately the same proportion as its weighting in the Index
If it was all computerised Vanguard would not need to employ 17,600 people.
On the second point first, I agree with Lootman's comment re the 17,600 people. That really isn't a huge number given Vanguard's size, the number of countries it operates in, etc. According to Wikipedia it had $5.3 trillion of funds under management as of Sep 2018 and was the largest provider of mutual funds and the second largest provider of ETFs in the world (with Blackrock being the biggest for ETFs - I don't expect those ranking to have changed in the last 10 months). Once you get to that size stuff like IT department, compliance, client services, marketing, product development etc become very large on a global basis not to mention people working on the funds that are actively mentioned as already mentioned by Lootman and those aren't just in the USA, e.g. 6 equity funds are explicitly marked active on the UK web site here (https://www.vanguardinvestor.co.uk/what ... e-products
On the other part, just why are those "weasel words"? That's common practice for trackers. In fact I alluded to it in my earlier comment when I said that I look at "(charges, supplier reputation, sampling breadth, etc)" in considering a tracker. That last one, "sampling breadth", was referring to exactly this.
As I understand it for smaller funds trying to track an index with a huge number of components it is not always practical to hold every constituent where the costs of maintaining the correct proportions of all constituents at the frequency desired (ideally daily) might have a disproportionate effect on the charges and/or the smaller constituents, coupled with a smaller fund size, might make adjustment trades (as the fund size changes at the end of each day) unacceptably small.
I'm not sure if it's a legal requirement but Vanguard certainly disclose the information, e.g. for the one I mentioned in my last post The FTSE Dev World ex UK index has (or had at time of Vanguard's last declaration) 2,043 constituents and the Vanguard tracking fund for it contains 2,080 different stocks (https://www.vanguardinvestor.co.uk/inve ... _fund_link
I confess that I'm not sure why the fund actually holds more stocks than are in the constituent index, maybe because of its global nature there are always things falling in and out of the index and this is some timing issue whereby purchases on newly-entered companies are made slightly before the disposals of stuff that has fallen out, or perhaps certain constituents are covered by holding shares listed on multiple markets. I'd actually be interested in knowing that answer if anyone can supply it.
For me as long as the sampling breadth looks to be at or close to 100% I am happy with it. If I saw a sampling breadth at 75% or lower I would start thinking that I should be looking for a bigger fund supplier that had the economies of scale (number of customers in that fund) to be able to afford a better sampling breadth or that I might be looking to track too esoteric an index if there was no other supplier with a sampling breadth that I was comfortable with.