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Yes, that's laminate.

Any place that does custom laminate (there are a number of brands -- Formica, Wilsonart, etc.) countertops will be able to do this for you at minimal cost.

definitely so - any cabinet shop could do this for you...and if you wanted, you could even switch it up and do a wood veneer instead. Since you are spending the money, you may as well go the extra mile and do a walnut top or something...

Show the photos of the table to the person making the new top, along with the measurements, and it'll be easy enough to replace. It's only laminate glued on plywood...
Flip the table over, and you'll see that the top is screwed on. Unscrew the top from the base, and replace top with new surface. Simple as that.
These MCM tables almost always had Formica tops....

The newest This Old House mag has a step-by-step on putting on new laminate.

How about going another route and doing a mosiac on the table top? I did it once on a table and it came out great. You can use older peices of stained glass or tiles (which you can get at a craft store or hardware store for the tiles) and focus on the colors you have in the room.

Personally, I would go to Ikea and get a table top out of the desk section (if you can find one that fits), or even a countertop out of the kitchen section. If you have to cut it, the kitchen counters come with the laminiate strip to finish the cut edge. This would be a cheap way to do it yourself and get the look you want. If you don't have a saw to cut it, home depot will do it for a few bucks or there are even tool rental places.

Another idea is to hit salvage yards like Urban Ore in Berkeley and look for a stone slab or tile pieces. Could be a unique solution. Good luck!

Room and Board sells tabletops in several sizes and shapes and about a dozen materials/colors.