I run a site that provides counter information for League of Legends (http://www.championcounter.com/) and I doubt very much my users will benefit at all from me moving over to HTTPS.
Switching over to HTTPS in and of itself shouldn't stop much data leakage given that the hostname - at least at current - isn't difficult to obtain (and really gives the game away for the content you're visiting as far as my site is concerned), but I suppose it's a step in the right direction and will stop primitive tracking attempts.
Protecting against code injection is actually a fair point though.
Sure they would benefit. They could check whatever is on your site without anyone in between noticing (WLAN e.g. at starbucks, corporate LANs and the proxies used etc etc). There are companies out there, who buy surf-habits (read: browsing logs of URLs visited) and mine it for valuable data.
Also some isps have been caught injecting ads into plain text web sites [1]. Do you want more ads on your site that you didn't put there?
[1] http://zmhenkel.blogspot.com/2013/03/isp-advertisement-injec...