I'm not sure if the tunnels change anything, but assuming they're up to some sort of code, probably nothing.
Genuinely curious to why that would be? Subsidence?
Even if the market is super hot right now and it seems like people will buy anything, anyone who looks at buying this will definitely be thinking about how hard it will be to sell in 10 years when the market isn't so hot. Most likely 90% of them will either back out or demand discounts that basically assume the whole thing is a mess and will need to be ripped out by professional contractors.
They list all kinds of small details: a single double glazed window containing condensation, or a gutter leaking onto an exterior wall. Experienced buyers would know which of the details are actually important, but it's still a sobering document. They encourage buyers and mortgage providers to act cautiously and are typically used as a tool for negotiating the price down.
If you are a cash buyer and just don't care, then fair enough. But whether or not it's a sound piece of engineering, a DIY tunnel (without planning permission?) dug underneath the property would be a massive red flag for your solicitor and your surveyor who would likely provide professional advice against buying the property. And mainstream mortgage advisors and insurers and may even refuse to do business with you due to perceived risk.
That said, I have trouble believing in the current insanity of urban property markets that anything could make a regular house hard to sell. It won't make it more valuable (nobody's shopping saying "I really need that underground bunker") but I seriously doubt he'd have any trouble beyond that.
He's done way too many projects that involve just generally making your life a bit difficult.
Or has a kid who's in the same situation...
Say you're in one of many low to medium density areas (sf, suburbs of nyc, etc) and need more living space. Going up is very expensive and causes conflicts with the neighbors (earthquake zone, views); down is even more expensive; building in the yard loses, well, the yard. So going under the yard is not a crazy option.
Particularly in our brave new wfh world where employees now have to pay for their own working space.
See also Fred Dibnah's attempt to build replica coal mine (with 30m shaft) in his back garden, using only techniques and machinery contemporary to the period[1][2]. Sadly he passed away before he could complete it and the property has had a strange history since then.
[1] https://www.youtube.com/watch?v=tqAbMbRQ3jE
[2] https://en.wikipedia.org/wiki/Fred_Dibnah#Dig_with_Dibnah