For me, the articles show
1) They're competent. If they're experts at solving all these random problems in managing a Linux server, they probably also know how to run a reliable, high-performant VPS.
2) They care about their customers. They're going the extra mile to help customers (and potential customers) solve their actual day-to-day problems. This is a good sign.
Haven't yet had an actual problem that required me to contact their support (which hints at #1), but it's the impression I (and probably many others) got from the articles.
I'm just glad they actually took that idea from them and anybody that provide any services should have these tutorials... It makes it much more approachable for people with little system admin skills.
DO has a dedicate team just providing incredible tutorials that are somewhat related but not completely related to DO itself.
If you google for some standard server maintenance problem (e.g. migrating from Apache to nginx), it's usually DO which is ranked first. Their posts are relatively high quality, and there are a lot of them, enough to cover many common problems. For example: https://www.digitalocean.com/community/tutorials/how-to-migr...
It doesn't show annoying pop ups, anything like that, but after visiting those pages many times you might decide to give DO a go. Well, that's what I did.
Also, some people say that similar cheap VPS providers exist for a long time and what DO did was put a nice simple UI. That proves that to create a successful product, you don't need some new complicated features that your competitors do not offer. Making interactions with the system easier, improving user onboarding process by reducing friction can go a long way.