I full-on support the idea. So far I've always googled "Darebee video" + name of the workout, which can be a hassle after a while. Just a list of links posted after the timer would work (not sure whether the current page layout allows for text tho).

Have you seen the exercise library with the videos? There is also a search function to look for specific exercises. Maybe that's a bit easier than searching via google

And I think the idea with the linking within the program pages is pretty cool! But I think it would be quite a lot of effort to program that, because the workout of the day is currently entered there as an image file. That is, the image would have to be separated, entered individually and provided with the link

Well, let's do some math:
There are ~1700 workouts in the database. Some have 9, some have 4 exercises. Let's go for an average 6 per workout. That's 102000 exercises to map, link, check... Since all the layouts differ, that has to be done manually. Let's say 5 minutes per exercise. Assuming a 40h week, we'll end up with one person doing nothing else for 5 months.
And it would be just another source for bugs. If you look into this here section, you see how many typos and mismatched descriptions happen without HTML and SVG scripting. Just with a simple JPG.
I guess, even if somebody is new to callisthenics, usually they figure out quite quick how to do a Jumping Jack or a March Step. The avatars in the picts are really great.
Some stuff can be tricky and then there is a good chance that somebody else asked about it here before. So a quick Hive Search can help. If not, post your question in the Help Desk. I am sure somebody will answer shortly.
Do not forget, that this is a free, donation financed site. I'd rather have the beekeepers using their time coming up with new exciting workouts and keep a tab open with the video excercise library, that mixtape pointed out.