As explained in how C2 licenses work the company/business license can be either attached to a single person or to a company owned computer (allowing any company employee to work on that station).
As you guessed yourself, getting the license from steam will require you to have steam installed on the working station.
If different people are to work at the same time on different instances of Construct, you need several licenses (one per person or per computer).
In the absolute, it's rather recommended to get the license from Scirra's website/manual installation. It allows you to keep up with the beta, execute several C2 instances at the same time (Steam version allows you for only one), it has no DRM and supports better Scirra in the end (money is sent directly to them).
Scirra's store also allows you to get license and redeem them later/gift them. I don't know how this works with Steam's licenses. (Also Steam's licenses are not linked to Scirra's website/badges)
It sounds like that for your company case, you should buy four licenses for all four people to work on. For your own personal version you can go with the current Steam sale if it suits you, but be aware of the limitations of the personal license (you can't make more than 5000$ with it).
To make sure don't hesitate to send a mail to firstname.lastname@example.org to confirm the correct way to go according to your case.