So, how is it possible to have the same profit both at 70 and 80 units?
It is possible to have the same profit at different level's of output. Profit is given by:
$$\Pi = PQ - TC(Q)$$
Where $P$ is a price (which sometimes can also be function of quantity $P(Q)$ although this is not your case), $Q$ quantity, and $TC$ are total costs that depends on quantity.
Because $TC$ changes when $Q$ changes it is completely possible to have two different levels of output that give you the same level of profit. Your own table shows that when firm produces 70 quantity its total costs are 190 which means that average cost (AVC) of producing 1Q is $AVC= 190/70\approx 2.71$ whereas when firm produces 90 units total costs are 230 so $AVC= 230/80 =2.875$. In this case the more you produce the more it is expensive to produce. Hence yes you are selling 10 more units, but these 10 more units are also much more expensive to produce so your profit won't change.
Why the firm doesn't stop its production at 70 units?
It could stop there. The problem you show simply does not have any means of distinguishing between equilibrium where firm produces 70 or 80 units, so unless you add more information technically both answers that firm will produce 70 and 80 are correct answers.
You could expand model in ways that would allow you to make 70 unique equilibrium by for example adding decision rule that says that due to disutility of working firm will stop at the first quantity that yields maximum profit. The problem could be adjusted in various different ways.
What are its gains from producing 10 more units if it doesn't earn more profits?
There are absolutely no further gains of producing 80 as opposed to 70 units but there isn't any loss either. Without some further reasoning or assumptions either 70 or 80 would be the quantity that profit maximizing firm would pick because in the simplistic problem above producing 70 and 80 yields the same outcome. For example, if you are going back home from school, your house is on the opposing side of block of flats exactly in the middle (so going around left or right takes the same amount of time) and you want to minimize time traveled, you can pick either left or right and nothing more can be said until we start adding more assumptions (maybe the left road goes around garbage pile and right around park so right would be prefered).