Yes, attributes count and make up a significant portion of damage for everyone. From what I heard, regular armor as well as armor mastery attributes don’t count, but I haven’t personally tested this yet.
Plus skill levels from gear should work, as should bonus item properties (like Ignition again for example). All other stats that an item should provide, at least in weapons (the only thing I’ve tested along with off-hands) is standardized to give a set amount of damage or defense based on the type of item it is (all swords give the same amount of physical damage, all staves give the same amount of magic damage).
Monster gems work in Battle League, at least my Ausrine gem did in 5v5.
Finally and obviously, stat and skill points do impact Battle League to a degree. You will notice that even with no gear on, you’ll have slightly less HP inside the instance than outside the instance. But this does mean that a 280 player has a notable advantage over a 126 player queuing in, especially if the difference in points is placed in constitution, as well as a class level 15 having a notable advantage over a class level one of two appropriated jobs.