Just by the wording it shouldn’t matter that it’s 2handed. If you are checking your character sheet to see if it works, it might not be reflected there at all. A lot of conditional passives like this don’t show any change in your character sheet.
It applys to axes. I see a noticeable increase of hit and ailment application when using 5/5 blade master. What type of 2 handed axe are you using? Weapons each have a speed multiplier with two handed weapons usually having a multiplier that is worse than 1 handers.
For example the fastest base is a one handed sword at 1.2 ( scales attacks speed at 20% more total attack speed) while the slowest base is a 2handed mace at .86 ( actually lowers the benefit of attack speed by 14%). Most 2handed axes will actually lower their overall attack speed by 5% as they usually have a base of .95 although some are even slower than that.