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.
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!