I'm not really sure you can ask someone to type quieter without ruining their workflow or causing animosity between you two.
As a developer, I'd be annoyed if someone asked me to type quieter in a room with other computers, I'd not only have to be conscious of the fact that I may be too loud every now and then if I was attempting to type quietly, but it would also be distracting (for my thought process).
I'd understand if It was just me in the room in a library typing really loud across from someone, but this is the pain of working in an office sometimes. I'd recommend you get some noise canceling headphones or ear plugs.
As BillK notes in the comments:
Noise canceling headphones probably won't help in this situations. ANY over-ear headphones may help, but noise canceling is generally an active process that listens for a given noise and emits a counter-noise so it works best on engine and fan noise. It can work on crowd murmur noises, but not sharp clicks & pops.
So it may be better to use over-ear headphones for this particular scenario.
If you really want to approach the guy, you could go over with a few paper towels or a thin layer of foam to put under his laptop and say:
Sorry, my headphones are terrible. Do you mind putting this under your laptop to absorb the sound of the keys?
Obviously, you'd find a solution based on his reaction (I wouldn't mind as long as it didn't make the laptop uneven). But at least then you're going over to him with a solution to the problem rather than simply pointing out the issue of his typing. If he says yes, he'd be much more conscious of the noise and may even type quieter afterwards.
Or depending on what you know of the guy, you could go over with the problem and then offer the solution as mentioned in the comments by @DavidZ
Hey, your keyboard is loud, is there any way you could keep it quieter?
instead of approaching him with the foam and directly asking him depending on his reaction, you can then offer (or go fetch) the foam if you wish to do so.
Also, get a piece of card (or paper) and fold it up and stick it under the table leg that is uneven, that'll help stop it from wobbling.