How to fix gaps in shelf without a table saw?
Option 1:

Disassemble the left portion of the shelf.
Cut all shelves to the same length as the shortest shelf.

It seems that you'll need to make a notch at the back edge of the shelf to wrap around the vertical support for the right side shelves.
It appears that the largest gap may actually be at the bottom - use this gap to shorten the rest of the shelves.
If necessary, cut the left-side back to match this length.


Reassemble, ensuring that the shelves on the left match up with the appropriate shelf-face on the right.

Option 2:

Move all the shelves on the right up or down a hole or two so they don't line up with the shelves on the left, thus hiding the fact that they don't meet up.
Arrange your storage so that this mismatched height becomes &quot;necessary&quot; due to the mismatched height of things stored.

Option 3:

Buy wider shelves for the right side so they butt up against the shelves from the left.

Material may not be available in stock form at your local supplier in the 1/4&quot; - 1/2&quot; wider width you need, you may have to buy something 1&quot; or more wider, then rip the back edge down to get the exact width you need.
Ripping the back leaves the white melamine covering on the front untouched so it still looks nice, and it helps hide any slight wobble in your rip cut of a long board.



Finally:
None of these cutting options require a table saw. (The rip cut suggested in option 3 would be easier on a table saw, but it's not required.) As a matter of fact, a table saw is the exact wrong tool to make a crosscut on a long piece of wood like a shelf.
You would want to use a circular saw, jig saw (prepare for a shoddy looking, uneven cut) or even &quot;just&quot; a hand saw for these cross cuts. You could do the rip cut with a hand saw, too (been done that way for centuries before they invented electricity...) if you wanted to.