My mum died from (not with) dementia.
Quite often they will die from something else first, but if there is nothing else then, yes they die from dementia.
Unfortunately, dementia is a condition where brain cells atrophy and die. This affects memory, but not just memory because the brain cells dying happens eventually throughout the brain, so everything - logic, reasoning, ability to perform tasks, mobility, behaviour, speech, continence - all go. Eventually the dying brain can no longer control all the body functions and they start slowly to shut down. Finally the swallow reflex is lost and breathing and heart beat cannot be maintained.
This is very, very different from normal aging. The popular picture of people with dementia just becoming more forgetful and fading away is far far from the reality