Have you purchased these mast steps already? Looking at their web site, I don't see how long the supplied screws are. They are a M6 - 1 flat head, but that is the thread size and pitch. It does not list length. My guess is that they are long enough to protrude inside your mast. Not knowing their length, I can't assess how much that may be but may be similar to what a rivet would protrude. I don't know what you've got.
Riveting on mast steps is quite common. I've never done it any other way. Personally, I would prefer to use monel rivets. But your screws will work just fine.
Its my understanding that screwed or riveted structures of this type are fairly similar in strength. But that's at initial installation. However, in this installation, the loadings are primarily shear. There should be little difference in strength between a rivet and a screw. It does take a fair bit more time to do the installation with the screws as you need to both drill and tap the mast for the screws. Alignment is also critical, much more so than riveting.
As said above, you really need to apply either tuf-gel or lanolin, some kind of isolation coating or in short order the removal aspect of your screws will not exist. I'm assuming the screws are 316 stainless steel. Do you know beyond just stainless?
dj