this is all getting very confusing....
The start at 09:02 has two options, one with a short connection at Spiez and a huge one at Domodossola, the other with more time at Spiez and still over an hour at Domodossola. The overall journey time is the same. The first option uses the Lötschberg Base Tunnel and misses a huge amount of scenery, the second uses the classic route with the scenery and the short original Lötschberg tunnel.
The 09:37 option also uses the base tunnel, and adds a transfer at Brig into the previous option coming over the classic route -after the scenery. All three go through the Simplon tunnel.
There are also two options shown at 09:25 via Luzern and Arth Goldau, both use the Gotthard base tunnel (which misses much of the scenery on that route), the first gets you to Milan faster but there is a very short transfer at Lugano, the second is less hectic and is a direct train from Arth Goldau to Milano.
As WengenK points out, there are direct trains from Spiez to Milano that would make it a much simpler journey - but not around that time of day. It would be a start at 07:02 or 11:02 instead - and they use the scenery avoiding Lötschberg Base Tunnel.
The optimum itinery for ease and scenery is to set departure to 10:02 with a specified route of via Kandersteg, which puts you on the international train at Brig and continues beyond Domodossola to Milano. This means you start one hour later, get the scenery, miss the transfer at Domodossola and are only 20 minutes later into Milano.
As for the confusing message about Italian check-in, I'd like to see it in context - this sounds like a route generated message that isn't always relevant to that ticket (like telling you the toilets aren't working at a station you won't be using anyway). As far as I can tell that rule is for Italian "Digital Regional Tickets" not International or Long Distance tickets that happen to use a regional train.