The master link that came with my chain won't fit I have this master link that came with my chain (Snap On type). In the first picture it is distinctly the one on the left - not a spring clip.

Try as I might - it doesn't seem to be long enough? Do I need to use those funky chain pliers for it? How much can I compress that link? Thanks.
You need to bend the chain. Look at this link (PDF) for the Connex Snap On which is the same idea. The PDF is reproduced below in case the thing goes down.





As an aside, you normally can get an alternative standard quick link (like a SRAM 8 speed powerlink) for these chains, rather than the Snap on type.