With geometry you can create something that looks like a computer, but without the numbers it's just an Etch-a-SketchTM
A "computer" based, not on numbers, but on geometry alone is capable of only one thing: geometry. It could draw circles and lines at intersection points that permit the expression of angles, but you can't do anything more because there isn't anything more. Technically, it can't even draw circles with a given diameter because, while you can know that one circle is larger than another via geometry, you cannot know how much larger, and therefore cannot draw a circle with a precise diameter.
How would such a "computer" work? Not unlike an Etch-a-Sketch where, by trial and error, a series of basic gears and levers would drive the drawing knobs for the purpose of drawing circles and straight lines.
This, of course, isn't a computer as nothing is computed. It's nothing more than an underdeveloped plotter.
Computers aren't really about differences, they're about fractions
It would be wrong of me to say computers aren't difference engines. That is the result of what they do. Even our modern CPUs are little more than very capable difference engines. But the reason they work, the basis of their methodology, is fractions.
The difference between the count of teeth on two gears is a fraction. The difference between the diameter of two gears is a fraction. These two concepts were fundamental in the development of Babbage's analytical engine. He certainly stood on the shoulders of Euclid when he created his machine, but his machine could not have existed without numbers, and more importantly, fractions.
If you think about it, you can use geometry to divide a circle into halves, thirds, quarters, etc. But that has no intrinsic meaning if you can't express the idea as 1/2, 1/3, 1/4, etc. How do you create a computer that can divide 77 into 99 if all it can do is draw circles and lines? Eventually it needs to count the number of pieces it has.
It's hard to imagine a society that cares about geometry but doesn't care about running numbers
And by "running numbers" I mean the black-bag work accomplished by mugs in a mob who are taking the poor for their last dime in an illegal lottery.
It could be argued that modern mathematics descends solely from humanity's intense desire to know what time it is (I'm getting to running numbers). Geometry was certainly involved because arcs and lines were used to deliniate the passage of time in its simplest way: the passage of a shadow. But you can't use geometry to express what time it is. That requires numbers.
Of course, once employers knew how to tell time within reason they had the ability to pay their workers in proverbial bushels of wheat per-increment-of-time.
And that meant that some poor schmuck had to keep a record of how many bushels of wheat had been paid to the workers and how many bushels-per-increment were being lost to unproductive workers and gee if I just happen to smudge that number right there I can take an extra bushel for myself.
And that meant that his friend, who happened to know a couple of big honking Tongans, could lean on his I-keep-an-accounting friend (let's call him a "bushel counter" or a "bunter" for short) to get a few extra bushels for himself.
And that meant, obviously, that even more bushels could be had if we set up a raffle to win this handy-dandy flint-and-iron set if you just put a cup of wheat into the pool...
Wait... how many cups of wheat are in a bushel?
Geometry would let you create a machine, but without numbers (especially a knowledge of fractions) you couldn't do anything useful with the machine except draw more circles and lines.