To be fair merchandizing of Clan items isn't a new thing. The Recguide for the Peregrine mentions a small "chibi" plush model of the Peregrine called Uhu which regularly shows up in Mech cockpits and other places. Which isn't the only one in the series but it seems one of the more popular items.
Perhaps I was a bit unclear when I mean "entertainment-starved" but from what I read it seems more that even Clan entertainment caters to the education and indoctrination rather then "pure" entertainment. Perhaps something more akin to arcades or virtual worlds which (from what I found mind you) seem to be rather absent from Clan worlds (though might exist in their OZ's). Remember, Chandrasekar Kurita began dealing with the Clans and he didn't sell them high tech items but rather consumer electronica, toys and other consumables. Stuff that was rare among the Clans.
Hitting a sweet spot between education, indoctrination and entertainment is not that hard
Clan entertainment industry has been in business in the Inner Sphere for a century now, they would have gradually evolved and adapted to new environment without issues, they had more than plenty of time
As for consumer items it's less about availability and more about novelty
Clans have consumer electronics, toys and all other other stuff one might want but variety would on the lower end, different products from different manufacturers will always be interesting to people
Take a kid from the usual toy store to a new one with completely different toys and watch it go bananas
As for videogames they would have plenty of them available at home (game consoles, computers or online games) but arcade cabinets would be something completely new and a popular import item, you are spot on there