Your explanation of Ethereum, as a non-technical introduction, is fine.
The question has some resemblance to a very non-technical introduction to Ethereum, that compares Ethereum to the Internet, concluding that Ethereum is not a replacement to the Internet, but adds a significant dimension to it.
What Ethereum means for computing is that new types of applications and systems can be built. For example, before the Internet when someone wrote a program, they had to physically put the program on a disk and give the disk to users. With the Internet, the program can be placed on a server, and anyone with an Internet connection and a web browser, can access the program. But the server can malfunction, be turned off, or tampered with. With Ethereum, the program is on every computer in the network, so the program can only stop working if everyone decides to turn off the network.
Underlying Ethereum is a single, global blockchain database and can have meaning for the Internet of Things (IoT), because it will be useful for IoT to use a single, shared database, instead of each device being disconnected from each other by having their own separate databases and networks. The blockchain's unmatched uptime has been mentioned, and it is also not owned by any single entity or group of entities, so there will be no issues of CompanyX (who may have owned the database had not it not been a blockchain) from allowing CompanyY's devices to work and access the database.
On a more technical note, you're right that HTML, CSS, JS are still used in Ethereum and that browsers can point to Apps and DApps. Since current browsers don't have functionality to connect to the global Ethereum network, people can run DApps using the Mist browser which has a built-in Ethereum node (Geth).
Finally, a technical note to clarify: "They can earn Ether by commissioning their personal machine to work a day job and help manage the whole World Computer with everyone else." The World Computer is currently a consensus (an agreement) of all computers (that are on the network) on the result of computations. Note how this is different from the simpler view (which is possible in the future) that each computer contributes some processing power to the World Computer, and that the World Computer is the sum of all that processing power.