I could be wrong, but it's probably something about your phone's Safari settings. iPhone are very common. So, if others were having the same problem, we'd be seeing more complaints.
Just to go over it, based on what my settings are on my iPad (I don't have an iPhone but they are pretty similar):
o Under Settings(app)->Safari -- "Privacy & Security" -- Block Cookies is set to "Allow from Websites I Visit"
o Settings(app)->Safari -- "Advanced" -> "Website Data" -> "gametz.com" try "edit" then
-> Delete to remove it for gametz. That should remove cookies.
Based on what you wrote, maybe you did this already.
I use Chrome on my iPad most of the time, but I am able to sign on using Safari. Initially, I did have some trouble signing off. It let me, but then I was still signed on (stuck cookies). Using "Clear History and Website Data" from the settings app Safari page cleared that. Also, deleting it specifically from advanced also worked.
Closing Safari or rebooting your phone may help if it's somehow some stuck state thing.
If you get really desperate, I could try to give you a very insecure sign-on link (like the good ole days).