Armchair general here, but if i were to guess israel’s plan:

The northern part of Gaza is where the majority of rockets get launched, since they have geographical proximity to several israeli cities from there. IF israel annexes north gaza, that would already be very changing to the military situation. Hamas can obviously launch stuff from south gaza, but the geographical distance to israeli hotspots dramatically increases (by itself an obstacle), AND norh gaza can be transformed into an extended Iron Dome with several military facilities in place to act, not to mention that now Israel only has to watch half the terrain.

The heretofore events point to this possibiliy, since Israel gave the ultimatum to evacuate northern gaza, and south gaza for now seems to be spared from this. Of course, if Israel then eventually proceeds to colonize north gaza with new settlements (aka West Bank 2.0 electric bogaloo) , hamas has a new ‘easy’ target to hurl stuff into, but the military infrastructure in place will be much more impenetrable, and the local jews would be staunch sionists that accepted the risks and have high morale and preparations to deal with this, and not the mainstream israeli society.

Large library of games is factually incorrect, you just do not know the scale of games in existence. Far more titles in Steam, gog, itch io, and with emulation this all goes to the square power, the largest library of games is a PC.

PC gaming is actually a competitive market that would still give players options to escape that (Gog, steam, Epic, itch and humble dumble, hell even Microsoft store and company launchers), it is not guaranteed to never happen because cartels happen, but it is far more hard and improbable than consoles, which are locked-down computers with unbreakable monopolies installed in then, at the mercy of the feudal lord of choice. PS: not to mention, Piracy, emulators and Libre games on linux.