Why would a rise in interest rates slow them down?
Any increase in the cost of capital affects everyone. If there's an interest rate hike soon (and it's a big if given the fragile nature of the global economy) and if that causes Amazon to increase prices (a much bigger if given their historic willingness to tolerate margin-free growth and their regularly recycled story about AWS costs always going down) then those businesses thinking about buying their own gear instead will also have higher financing costs to contend with.
If, on the other hand, AWS take a decision not to pass on those cost increases then the TCO analysis will move in their favour. Microsoft have already demonstrated that they'll pour huge amounts of money into cloud to try to stay relevant and that will likely keep AWS from raising prices even if they feel a pinch from interest rate rises.
I'd say when interest rates go up that's when things will start to look even bleaker for DMC, HP, IBM et al. as their shareholders have much less tolerance for eroding margins.