For example, my company matches donations to qualifying charities dollar for dollar. If I donate $100 and they match $100, can I count the matched funds as part of my masser obligation?
The definition of matching funds is money donated by someone else to match money that you have donated.
Matching funds are funds that are set to be paid in proportion to funds available from other sources. Matching fund payments usually arise in situations of charity or public good. The terms cost sharing, in-kind, and matching can be used interchangeably but refer to different types of donations.
Thus the money is not considered part of your ma'aser. One way of considering this is that as you get income you take 10% of that income and put it in a special account. Whenever you donate, you take money from that special account and send it to the tzedakah that you are donating to. Since matching funds are sent by someone else, they would not be taken from your ma'aser account but from that of the other person. If you had pledged to match someone else's donation, that matching amount would come from your ma'aser.
Note that if you had not donated, the matching funds would not have been sent to you.