It's tough for a casual game designer at the moment because Adobe Flash is by far the most powerful game design tool for casual games, but it has one major issue: it doesn't work well with phones and tablets. With Apple devices, although you can use Flash to create an app, Flash doesn't run on the browser at all.
Hence a lot of Flash game designers are turning to HTML5, an emerging technology that works well on mobile and desktop. Unfortunately, it is MUCH harder to make a game using HTML5. HTML5 is good for simple games but a royal pain to use to create more complex games. You need many more lines of code and there is no visual editor available. It is also more difficult to protect your games using HTML5. I want my hard work to be featured on my own site and not some Russian scam site.
HTML5 does have one great feature. You can create a game 'canvas' that adapts to the player's screen size. For example, the same game can be played on mobile and desktop and the screen size will adapt. This is called responsive design and I have done it with this game:
However, again, changing the game's screen size means you can only use this method for very simple games.
So where does this leave a site like FlashByNight.com? A lot of people visit the site on a smartphone or tablet.
The only way ahead that I can see is to feature some simple games for all platforms, while the more complex games will remain desktop/laptop only. Hopefully then, no matter how people log on, they can still have fun... that's what games are all about.