Why do you think you are more secure with web version? The game is still downloaded, and it can just as well have viruses. I often prefer download version because it can be higher quality, and yes it can have viruses like every thing else on the internet.
I have not seen any of virus alerts of trojan horses, but it's sadly possible there are some bad games. Most virus alerts I have seen is about the games is nearly never downloaded, and therefor it's not recommend by the browser to download them. They can of cause be bad games, but there is no way to know if they are good or bad.