don't take it personally, babe, it just ain't your story partially uses the "traditional" VN style, but also makes heavy use of an onscreen phone feature, which is used to give information in another way besides through dialogue. It also allows themes like online privacy to be explored a little bit. This one is rather long and it would take you several hours to reach an ending, but playing for just a few minutes would give you a good idea of how the phone mechanic works.
Nightowl and
.help by Mikomi both use a chatroom mechanic. It's similar to a traditional VN in that you simply click to advance the text, but everything is drawn so that it looks like an actual chatroom. Nightowl uses only the chatroom mechanic, while .help switches between that and traditional VN setup. Both are pretty short and you could quickly play through either or both to get a feel for the chatroom mechanic.
Her Tears Were My Light utilizes a really cool time travel mechanic. You can travel back in time and change the decisions that you've made; however, reaching a certain point before rewinding also adds new choices that you didn't have before. (I should add that the "tutorial" for this mechanic is perfectly worked into the story, so it doesn't have to pause and say "THIS IS HOW THE GAME WORKS.") The main menu screen also changes based on which ending you've most recently achieved. One route is pretty short and easy to complete, but I would recommend playing through all the endings for the full experience and understanding of the time travel mechanic. (Also, it's a super cute story.)
I woke up next to you again. actually doesn't deviate all that much from read text, choose option, but it's all drawn so that it looks very dynamic and it doesn't actually feel traditional at all. One playthrough takes only 5-10 minutes and I would highly recommend getting all four endings. It's a really meaningful game and definitely one of my favorites of all time.
Natalie and
Nobody Understands MIA by kenibatz both lean more towards being games than pure visual novels, so they might not be exactly what you're looking for, but they do showcase what else you can do with a game. Both are pretty short. Natalie is another personal favorite.
Put A Sock In It! is a lot of fun; it starts with you picking two characters to star in the scene. At certain points, three options will come up on screen and you'll have to choose one. The branching gets pretty crazy at times and it takes a lot of dedication to get every ending, but the way choices are done is really interesting as just one different choice can lead to an entirely different ending. As mentioned before, it will take a very long time to get every ending, but playing just a few will give you a good idea of how the game works (and hopefully you can find one of the morals).
What's Your Name? uses a personality test at the beginning to decide which route you'll play. It takes a bit of tinkering to figure out which combinations you'll need to get on each route. After that, the route gets interesting as the questions are timed, so pressure is put into the player to answer each one before time runs out. To make things more high-stakes, sometimes the best answer is not to answer at all. One route in this game is fairly short; it will take longer to play the game to completion (i.e. get all three routes, and the best endings, and see the game's epilogue). However, you can gain a good understanding of the game's mechanics with just one or two playthorughs.
Who Is Mike? also uses the tactic of timed choices, mentioned above, and additionally has an unusual protagonist. I don't want to spoil the VN so I won't say too much here, but everything combines into a really well-done story. It would take quite some time (and probably require a walkthrough) to get every ending, but playing through a couple times will give you an idea of the story and mechanics.
Where the Sun Always Shines uses speech bubbles instead of text boxes to show who's speaking. I haven't personally played this one so I can't attest to its length, but I have played other VNs by ebi-hime and they're always excellent.
