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If you want to close steam, right click on the tray icon and select Exit.
You can make a suggestion in the suggestion board to have an option to alter the behaviour of the X top right. But as it is, it works as intended in Windows protocols. So, Steam literally respects your wishes, it's just that you kinda got your wishes mixed up.
HOWEVER there are plenty of other programs that have the option of closing out completely and Steam should definitely have it and it's been requested for like a decade now.
Steam not fully closing on pressing the X is not a problem, it is a feature. That many programs have and share. To actually close the program you select exit or you right click the icon in the icon bar and select it to actually close. If everything else fails you simply go to the task manager and kill the task.
If my memory serve me correctly I think I've seen this kind of behaviour as far back as Windows 95.