On the lesson for basic sentences 1 it has chart that seems to imply the plural in Klingon is singular. I am probably missing something, but why is this?
I'm not sure what you mean by "the plural is singular." There are three plural suffixes in Klingon, plus some special words. Use the suffix -pu' to pluralize beings capable of using language (e.g. HoD captain - HoDpu' captains). Use the suffix -Du' to pluralize body parts (e.g. DeS arm - DeSDu' arms). Use the suffix -mey to pluralize anything else (e.g. Duj ship - Dujmey ships).
In fact, the plural suffixes are usually optional in Klingon. You can use HoD to refer to one captain or multiple captains. Maybe this is what you meant by "the plural is singular": you can usually leave off the plural suffix and still be grammatically correct. HoD vIlegh means both I see the captain and I see the captains, and you'll need some further context to be able to tell which one is meant. But if the plural suffix appears, the word must be plural: HoDpu' vIlegh can only mean I see the captains.
There are also some words that get pluralized irregularly. peng means torpedo, but its plural is cha torpedoes. Such inherently plural nouns like cha are always treated grammatically as if they are singular, even though they represent plural concepts. If you were to put a plural suffix on the singular form of such a noun, the noun gains a connotation of "scattered all about." For example, pengmey torpedoes scattered all about. You also get the "scattered all about" meaning if you put -mey on a regular noun representing a being capable of using language (e.g. puqmey children scattered all about).
Most (all?) of these concepts are introduced in different lessons. For the purposes of Basic Sentences 1, just understand that the suffix -pu' goes at the end of a plural noun representing a being capable of using language. I don't think Basic Sentences 1 will let you drop the optional plural suffixes (though it should).