Like most others I imagine, I just use MAL. I'm aware there are a lot of competitors out there trying to bring their own spin, but I've been a lazy consumer and not really done much researching into what they're offering that's different enough to warrant switching over.

(edit: I wrote this before hitting the form submission and so hadn't seen the kickstarter page you linked where it's pitched as an extension - I had assumed a web application competing with MAL instead.)

Here's some ideas on this space I as a casual-but-use-nearly-everyday user of MAL can offer:

1. The Dub-watching community is not supported well by MyAnimeList (which tends to favour Japanese). It is not easy to discover/filter which shows are dubbed, titles in my list are in Japanese names I don't associate with what I watched. This may be an opportunity to capture a niche away from MAL. People new to anime who aren't already entrenched from years of using MAL also (anecdotally speaking in an anglo-majority country) prefer English-first and dubbed content.

2. While MAL has community-driven reviews and scores, it does not have good systems for users to present their anime from a personal recommendation standpoint. Users will link their lists, and the only metric available is score and what they watched. User profiles are a little better at linking to favourites and reviews, but I think having a unique take on this at-a-glance splash page of information would not only be enticing to the users, but drive increased sign ups from people clicking the links and wanting to make their own. Consider a little customization, letting users feel like this is a page -they- made will increase retention as they spend time tending their garden.

3. If you're intending to support show discovery/reference: MAL doesn't do a good job of telling you where you can watch something. Directing users to streaming sites such as Funimation, Netflix or Hidive would be useful. Being able to filter to the services I already pay for would be helpful. Related, but Hidive has integration with MAL ratings currently - I am not sure if this was successful for them or not, but worth researching.

4. In terms of user engagement, you want to make hitting that "Episode Finished" button feel good for the user. As simple as it is, I already get a nice feeling of satisfaction as I tick the number up on MAL. Leaning into that encourages people to keep coming back to your website regularly. It will also produce more accurate data if checking that box off is one of the first things users do after finishing the episode. Consider making this moment lead into other experiences on your site or others. Maybe completing the episode shows you links to discussion threads for the episode. Maybe you can take a moment to write a quick comment about this particular episode. Something to make hitting the button feel good.

5. Another avenue to bring in users is stats & stat analysis. While new-to-anime users will benefit the most from seeing their "anime life journey" unfold, long-time fans have friction for their existing catalogue (they won't see a "journey" unless they really take the time to try and recall when exactly they watched a particular show). Getting them to input their data to see what sort of cool analysis and/or recommendations the site can give is a nice carrot to entice them in. I know anecdotally that the only time I tried a MAL alternative for this reason, and it provided an import tool so that friction was further reduced.

I mentioned in my form submission I'd be hesitant but not completely opposed to paying. I think you're going to have a hard time asking the users to be your direct revenue source when, as you say, there are already a lot out there on the market, including the top dog.