How can I remove tile grout from floorboards?
Scraper. This is going to be a tough job if you want to keep damage to the wood to a minimum. It does look like the floor has some type of finish on it before the grout material was applied. This should help a lot to make the scraping removal a bit more practical. 

Note that what ever type of scraper that you use will likely need replacement or resharpening a number of times in your removal process.