Ru after a verb?

…どちら が まちがって る と 、そち は おもう

Can you explain to me the use of the る in this sentence?

へいか は 、なに を おさめて る んです か?

Here’s another example. I would expect the conjugated verb to drop the -ru. What am I missing? Thank you.

る is a contraction of いる. ー(っ)て いる is a common expression to indicate a state or continuing action. In conversation, and very often in texts too, it is shortened to てる。
For example “What are you doing” would be as (or more) often なに(を) してる? as なに する?

So the sentences before the contraction are:

どちら が まちがって いる と 、そち は おもう
へいか は 、なに を おさめて いる ん です か? or へいか は 、なに を おさめて いる の です か? (“ん” is a contraction of "の”)

You’ll see てる all the time. One can say it’s similar to “gonna” vs “going to”, except that てる is even more pervasive.

Thanks!