Legally I think you own the book, but not it’s contents? So legally it would be the same? (The content is copyrighted so you can’t reproduce it etc)
The real difference is in usage, with a book, even an ebook, if you have it you effectively own it. They can’t stop you reading it.
Unfortunately with games nowerdays everything checks in with servers or is online only, so if the publisher or distributor say so, you lose access. The only way round that is cracked copies or DRM free games like on GoG.