I always wonder what exactly did he mean. I'm not quite familiar with Smalltalk and CLOS though I have tried them. But after work with Erlang for a while made me think I'm slowly getting what he said. I found these ideas are really fascinating.
Try to think about the following pieces:
1. A bee dies, the hive won't explode. Millions of cells die every minute within you.
In Erlang, usually, processes (object) are mostly organized as a bureaucratic structure, which has supervisors letting other objects doing the actual job. If someone dies or fails, the supervisor could just kill and replace them. This really looks like biological systems or human society. Not in a world that the boss let someone do some work, then the boss and the worker along with a whole world explodes if the worker fails (99% of OOP languages exception handling are not OOPish at all, it's totally imperative instead of modeling the relation between objects).
These correspond to the biological metaphor in the talk from Alan Kay in OP's article.
2. You can find and talk to someone alive if you know his address, email or phone number.
Java has object reference but it's not transparent to other systems, there is always the 'outside world' concept in this kind of reference or pointer system, similar to ST monad in Haskell. For a normalized database, there are transparent addresses for entity records, but they are dead and cannot talk to anyone until every time you need it, you sort of revive then interact with it for a short period, then you kill it and take its guts back to the database.
In Erlang, you can register any process (object) with an address like {user,42}, any other object can talk to it if they know the address, even from other servers. Just like how URL works mentioned in Alan Kay's talk.
3. The world is concurrent.
You have approximately a thousand audiences in a room. In order to count them, you let them all stand up. You tell everyone needs to get a number '1' in their mind. Then everyone finds another person, add their '1's, one person sits down, another person remains to stand, takes the former guy's number, then repeat the process. The last person stands has the count.
Usually, you only need to count very few times to get the answer. And this is what computer science is about. The problem is, that's not the way most computer program works. Because for most programs, even if you modeled 1000 people in Java, there's still only one person doing one thing at a time. Everyone runs on a monolithic thread. If you call libraries, you are giving them the most important thing you have -- the thread. And they don't promise they will return it to you.
Contrastly, in Erlang, every process (object) must have its own resource, no one can stop other people from doing things, no one can use up all the resources. The real world is a concurrent world where everyone is an isolated individual who can do things at the same time.