This service might work for online "Desktops" / Officwork,
watching movies and games with low reaction time (roundbased games, classic board and card games,)

maybe also for "low reaction time" games like WoW, RTS Games or
some racing simulations.
But not for quick-reaction time games as FPS.
No matter how advanced their architecture is, they
cant reach a latency-performance as on a local Lan.
The games will always feel laggy.

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But nevertheless, such a service will be appealing to
"some times" players. As they dont need to invest into gaming hardware. Or people who want to check out a game and
see if they want to buy the real one.

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To come around the problem of the lag, I have an idea:

The developers actually program a "gamelogic" plugin, wich
runs directly on the client machine.
This plugin calculates some of the gameaction on the client machine (given the userinputs), without the graphical calculation.
Then transmits certain gamestates to the server-"main" game.
This way it should be possible to resuce the lag somewhat,
as the userinput can be directly used to calculate a
part of the gamestate. Just the graphical feedback is slower
as it needs to go over the external server and back.