Hamachi was created by Alex Pankratov. Once LogMeIn purchased Hamachi, they ruined it with the following update (either purposefully or accidentally) by making it no longer work with a large handful of older games. That sanfu in combination with a more bloated UI, forced LogMeIn account, and a splattering of useless features made it obsolete within a few months. It was the fastest rise and fall of a piece of software I have ever personally witnessed. You can read about the original Hamachi on the author's website here: https://swapped.cc/#!/hamachi
LMI bought Hamachi in 2006 and I was involved in the development until 2009. Through that time there were no known issues with older games. Nothing was broken. What was tunneled before was still tunneled the exact same way, including IPX, IP4 broadcasts and multicasts. We did rewrite the client, cleaning up all the cruft, separating the engine from the UI, adding compression support and what not. It still wasn't fully integrated with the LMI core and no LMI account was required. The UI was redesigned in-house, without my participation, and while I didn't like the result, the original look wasn't a pinnacle of design either :)
What happened after 2009 I have no idea. The devs I worked with were really good, so if things broke, most likely it wasn't accidental.
I remember the UI change being around the time most things broke for me, and there were other users in the product forum with their various games also having issues. Maybe those type of posts were always numerous, and I never visited the forums before. For me the games that broke were Starcraft, Red Alert, and a handful of non-internet games. Perhaps the forum/customer-support tickets didn't make it down to you, but something had definitely broke around the time the UI changed.
It's likely the issues were quickly fixed and I am remembering the gradual post-2009 decline more vividly and blaming it on the time when the UI changed, which was emotionally upsetting ;)
But thanks for posting your remembrance of the events, and creating Hamachi in the first place!
FWIW I didn't use it until 2011, which sounds like it was years after the acquisition. It's always sad to see a beloved product go downhill over time, but at that point it was still pretty great.
Definitely look at ZeroTier--it is a perfect drop-in replacement that can be self hosted and the free tier of their hosted version supports 100 devices on unlimited networks. You can easily self host the network controller on a small cloud VM. Clients for macOS/Windows/Linux/iOS/Android/openWRT.
