|My question is this. Do you really need a laptop or will a desktop suffice?|
No laptop can perform as well as a well equipped desktop. The desktop will be more dependable, upgradable and cheaper too.
No integrated graphics can compete with the high performance add in graphics cards.
Don't get confused by specs on integrated graphics in laptops. Even if the model sounds similar they are not the same as a stand alone card.
The key in this answer is this except from your original post. "powerfull video card to run high demanding games".