The Reach is a major naval power in the books.
Spoiler
Tbh, I don't think there are more then 100-200 ships in that last shot. Let's just assume that they're doing away with logic at this point.
These guys have counted: http://www.thewrap.com/game-of-thrones-finale-how-many-ships-were-in-daenerys-fleet/
There are 350 ships in that shot. And let's not forget that the fleet does not end at the horizon.
Actually, I just looked at it again, and the fleet DOES END before the horizon.
Red is where the tip of the sails are, blue is where the horizon is. It does not extend to the horizon and it certainly does not go beyond it.
I did not count the ships, but they say it is 350.
I assume that about 100 guys are on each of those ships. Which is probbaly not the case... I tried to count the guys on GreyWorms ship and there are only about 39 Guys on the ship. Additionally, the ships are not specially large, and the guys on top of the ship do not seem to be specially crowded. In Terms of the Dothraki it is clearly less than 100 guys on each ship, the horses take almost all the space.
But just for fun, lets just assume each ship has 100 guys.
That "only" makes it to 35k Soldiers. Which is still insanely huge.