You are confusing physical possession with intellectual ownership. You absolutely own the plastic cartridge, the silicon board, and the physical state of the ROM chip. Because it is an offline, physical object, no one can remotely delete it. But you do not own the code, and you never did.

Under copyright law, ownership of a copyright is strictly separate from ownership of the material object the work is stored on. You own the material object. Nintendo and Square own the 1s and 0s.

You claim you never agreed to a EULA for Chrono Trigger. You didn't have to click an "Accept" button on a screen because the 1990s operated on shrink-wrap licenses. If you look at the back of the original Chrono Trigger box and inside the manual, the publishers explicitly laid out the terms of your limited license to use their intellectual property. The law didn't require your signature; breaking the shrink-wrap seal on the box or booting up the cartridge was legally recognized as accepting those terms of use.

Your house metaphor actually proves this point perfectly. If you buy a house, you own the wood, the drywall, and the land. But you do not own the architect's copyrighted blueprints. You can paint the walls inside your house, but you cannot legally take the architect's design and build an identical replica of that house on another lot.

You possess a physical artifact that grants you perpetual, offline access to execute a licensed piece of software. That is a great feature of the physical media era, and it is exactly why no one can take it away from you. But claiming you own the actual 1s and 0s because you hold the plastic is like claiming you own a novel's copyright because you bought a hardcover at the bookstore.