The author of the piece assumed 25M shares OS after the warrant exercise. It is not clear to me whether the OS count ended up being lower (21M) because 3.9M warrants expired unexercised or because he was anticipating that all warrants would be exercised and about 3.5M remain outstanding.
Either way, you can figure EPS against the current OS and get a higher number, just realize the pros are going to do their EPS modeling based on the OS count and the outstanding warrants.
All that aside, I think the real story here is the growth of the Macau gambling biz and the opportunity AERL has to do some consolidating with the $50M+ they have in cash. Over time this market is going to continue to grow, bolstered by the secular growth in China/Asia. Which is why you see LVS getting an absurd multiple. Obviously LVS' scale is way above that of AERL, but $55-60M in net imcome is nothing to sneaze at. That is why I believe the p/e will ultimately expand to something closer to 15x forward earnings.
Now the fun math. Take the low end of the NI range given in the recent guidance ($55M) and the current share count (21M) and you get $2.60 in EPS. This is back of the envelope stuff and certainly not spot on. That said, put a 15 multiple on $2.60 in EPS and you get a share price of $39.
Now you see why the stock is ramping so quickly.