It does look like 6 chairs will be tight, but you should be able to seat 6 or even 8 at a 60" round table. Are you sure of the table size? The chairs seem to push really far under the table too. I'm looking at the one on the right and even though it is not all the way to the table at the back, the legs appear to be all the way into the center. I just checked a number of chairs and found 18" widths pretty standard -- with one only 17". I have a 60" round and keep 6 chairs around it. We have 2 stools we can pull up to seat up to 8
Even with narrower chairs, you are going to have an issue with the spacing around the base. The legs of the chairs are going to compete with the legs of the table. Doesn't mean you can't do it -- just something to be aware of.
Q