Learn Russian: Они знакомятся на работе.

The suffix -ся usually makes a verb reflexive (doing an action to yourself), but here it makes it reciprocal. The verb знакомиться means to get acquainted with each other. The action is shared between the people in the Они (They) group.

I learned that to meet is встречаться. Can I use that instead of знакомятся here?

It would change the meaning! Знакомиться specifically means to meet someone for the first time (to get acquainted). Встречаться means to meet up with someone you already know, or to date someone. If they are meeting for the very first time at their job, знакомятся is the correct choice.

The lesson says reciprocal verbs often use с (with) plus the Instrumental case. Why is that missing here?

You only need с if you are specifying who a single subject is meeting (for example, he meets with Ivan). Because the subject here is Они (They) and they are simply meeting each other, the 'with each other' idea is already built into the reciprocal verb знакомятся. No extra preposition is needed!

Quick refresher: why do we use на instead of в for 'at work'?

In Russian, certain locations and events always take the preposition на instead of в to mean 'in' or 'at'. Работа is a classic exception. To say you are at work, you always use на работе (using the Prepositional case ending -е).