Day by day, the activity of the site is reducing. The number of visitors, the questions per day and everything is reduced.
The activity on a site in private beta is generally pretty strong at the outset and peters off after a couple of days, surging again when the site enters public beta.
Both of those sites you're referencing are very old. Game Theory started Private Beta in August of 2014 and How Things Work started in April of 2011. The process for betas has changed since that time, significantly.
Similarly, that blog post by Joel is absurdly old... from 2010. Look at something more recent because the way the ecosystem here grows is no longer based on that outdated post:
Past experience had led us to believe that “small” and “unhealthy” would mean the same thing: we took it as a given that quiet sites would develop spam and obvious broken windows, while high quality sites would always grow big and graduate. But you proved us wrong! Five years later, we have lots of tiny sites which have been in public beta for months or years, each consistently producing excellent Q&A which helps people with real problems. Small, consistently active sites are great!
I encourage you to read the entire post to understand how SE thinks about sites and beta and when to close a site or leave it open. I point your attention at the paragraphs here:
Thanks to many devoted users, it’s grown clear that smaller SE sites can do a great job of maintaining themselves and producing high quality Q&A. Not every site is going to be a blockbuster success, but our small sites are serving their own communities well. We’re proud of you, and we want you here.
What does this mean? If there's enough moderation for a public beta site to consistently remain free of spam, for flags to be cleared, and for our Be Nice policy to be upheld, your site will remain open. However, if community leaders drop off, flags sit without being addressed, and we can’t find any suitable volunteers to step forward, the site gets closed.
As of this post, not a single site currently active in our network is at risk of being closed. Closing public beta sites is a rare occurrence; we expect it to stay that way.
As long as users are doing their jobs, helping moderate the site, keeping it free of spam and other bad posts, the site traffic levels are less important... and our traffic is fine for a site in private beta! Don't put too much weight on the targets on Area 51. They haven't been updated to reflect the new thinking on site quality. Look at recently-created sites, and their stats, not sites that died years ago.
Encouraging questions is great but we don't need to have a big doom and gloom
WARNING WARNING WARNING
... because we're doing just fine.
This is an addition to Catija's awesome answer.
One thing that is not emphasized enough is that the Area 51 stats are not the best indicators of site health. From the beginning, it has been acknowledged that, as Robert Cartaino put it 6 years ago (original emphasis kept),
The Area 51 summary does not represent some sort of “report card” filled with pass/fail grades.
. . .
The Area 51 statistics provide an opportunity to see where your site can improve.
Those numbers don't matter. Well, yeah, they do - after all, they aren't random - but if you want to take the pulse of a community, you don't look at the number of clicks it's getting, or how many folks use it, or how many answers the average question is getting. Instead, you look at the content and the users.
There are two major reasons I've seen sites shut down in the past:
- The userbase is not equipped to deal with the site. In some cases, there isn't a huge expert component, which has led to poor questions. I believe this happened for Open Science, and Artificial Intelligence. Alternatively, people might have stopped caring. Seeing that can be heartbreaking. It can happen even for public betas - I see that, too.
- A lack of good content. If users are not creating good-quality content, then the site may not be making the Internet a better place, which is what we're all striving for.
But let's say that you're still concerned about activity. I've been through something like 10 private betas over the last three years, and almost all of them display the same trend: An influx of posts on day one, because people are curious and really, really, really want to ask their questions, followed by a sharp drop-off when the flow starts to run dry, and then a boost when the site goes into public beta and more users come in.
If you don't want to trust me, look at What is the typical growth pattern of a new beta site in the first few weeks? on Meta Stack Exchange - especially the answer by Gilles, which I have cited multiple times in the past:
This is a typical growth pattern for a Stack Exchange site. The scale is highly variable but most sites go through similar phases.
So, yes, this is normal.
Finally, if you're not swayed by the argument of "This is normal", I invite you to reread Catija's answer. Stack Exchange's position has evolved over the years. I remember being especially excited to read Graduation, site closure, and a clearer outlook on the health of SE sites, which made the new policy official: If a site doesn't display either of the issues I mentioned above, it's probably going to stay open..