Calculating Significantly Above Chance for 3-AFC Test
The hypothesis would normally be expressed as a one-sided test as p(X≥10). The online calculator you have selected is fine and the significant result could be expressed in an article as follows: (p=0.33, q=0.66, K=10, n=18, p-value = 0.043).  

Another way to think of this is that 9 or fewer correct answers is more likely to be random chance.

At the threshold of 10, it is unlikely that the result could be explained by random chance.