Yes
That is an unnecessary stamp in a box on a form that is no longer required.
I have not used a stamp for over 10 years (since DWP said that a stamp was not necessary).
You literally need to think outside the box! Just because outdated forms have a box for a stamp does not mean that DWP require a stamp. Have a go at them by all means for not updating their letters to reflect the relaxation in their procedures.
DWP of softened the requirements gradually in recent years, first saying that anyone who can countersign a British passport application can sign a Life Certificate. More recently they have said that anyone of good standing, not related to you, can sign.
I am sure that you are smart enough to understand that KannikaP is absolutely right - you might as well sign it yourself. This is just a tick box exercise and when the forms get scanned, when they are returned to Wolverhampton, nobody undertakes any due diligence - the system is simply marked that that pensioner returned the form.