Based on the type of fasteners, it appears you have a wood compression post.
Like Gene says, you'd have to fill the hole that goes into the compression post with epoxy +filler.
Once that is done, you'll need to pre drill a hole into it, a bit smaller than the lag screw.
If you just fill the hole and put the screw back in, the teak compression post can/will split.
For the deck portion of the both holes, I'd pot them with epoxy and redrill them. That way the core is protected.
Having the repaired holes in the deck lined with epoxy is the goal.
EDIT: http://www.pbase.com/mainecruising/sealing_the_deck
While you could use a short piece of wood dowel in JUST the top of the compression post, I would NOT use it to fill the 2 deck holes, since it can absorb water.
The Lag screw is the what attaches the mast step to the compression post. (the important one)
It goes through the deck, and into the top of the compression post.
The normal bolt stops the step from turning, and only goes through the deck.
If I remember correctly, it's recommended to use a slightly larger lag screw than original. I think the CD kit mentions that.
Not sure why that spacer block was added by a previous owner. I presume the mast was modified at some point. Maybe the bottom of the mast was damaged and it was trimmed shorter at some point, so the spacer was added ?
Maybe they added the spacer but didn't change the fasteners to longer ones ?
I can't see needing a new step though. Unless you want to upgrade at the same time, for things like the ability to attach blocks to the step. Personally I'd upgrade since you are already doing the work, but it's not required.
EDIT: If you decide to use Butyl Tape to reseal it, here's how to do it:
http://www.pbase.com/mainecruising/rebedding_hardware
Beware the quality of some butyl out there ! Some is not suitable for boats.
Some people suggest simply buying it from MaineSail, but other stuff is out there, you just need to test it before you use it.
EDIT: Both links BTW are by the sailboatowners.com featured contributor "MaineSail"