I second what aveoturbo said - your dumbbells are too light. (Are they adjustable? If so, you can just buy weight plates separately. If not and you're serious about working out with dumbbells throw away those disposable fixed weight dumbells - past a certain point they are nearly useless)
Another random guy suggested great workout routine with pushups - those are go-to bodyweight exercises for chest development.
Also Dumbbell Chest Press in Ironborn program is done lying on the floor which restricts the range of motion. To get the best from Chest Press you're supposed to do it on the bench, moving your elbows below your body level. You can take a look at a good chest dumbbell exercise selection here.
Good luck with your training.