Oh, it is safe. you get the link from the dev, after all. and only crappy if you push your users to their download limits or your service shuts your content down for you exceeding your own quota. I saw that happening on google shares.
What I deem rather unsafe, untrusty and a no-go is an update companion of a mere indie game. And most aaa games for that matter. Essentially bundling a download app for the app I want? Nah. I might trust a small indie game dev to cobble up a fun game. But managing a downloader and updater, complete with hosting as well? So I get infected with malware, when his update server gets hacked? Or he messes up my system with some update scheduler? And also trusting the dev not to use his infrastructure to secretly phone home some "innocent" usage data or do other questionable things, just because he has a bad day.
The problem i see, this is games we talk about. not an everyday usage tool like vlc. Or an online game. The need for an updater companion for an offline game makes me suspicious. a button "check for updates" might be ok, especially if it just opens a browser.
Using the devs homepage would be ok. For me. But I am curious, how op sees this.