That is not a freewheel, that is a first generation Shimano Uniglide cassette. The freewheeling mechansim is a part of the hub, and the cogs are removed with two chain whips. Assuming you bought a wheel with a threaded hub, None of the old parts would be compatible with your new wheel; you would have to buy a new 6-speed freewheel.

EDIT: Your new wheel likely has a wider hub than the old one. There are a couple of different ways to get it to fit into the old bike. If you elect to use the wheel as-is, you don't have to stick with a 6-speed. You can fit a 7, or possibly even a 8.