Umm, it's hard to provide specific examples because the information you gather from what I show would probably be different from the things that I feel need improvement. But let's take
this website as an exemplar for the type of site you're going for.
And let's take
this one as an example of a professional website that doesn't look or work very well.
One of the first fails you can see is that they're using a flash menu. Flash doesn't work on phones, and likes to crash, you honestly shouldn't be using it for something as important as the menu.
The layout of the front page is confusing. Why is there a random search bar in the middle of the page? What information should you be looking at first? Between 3 columns and 7 boxes (one of which isn't even used), along with several other images/buttons, the user loses interest and needs effort to browse the site.
There are even 2 different kinds of fonts on the front page. Inconsistency in a website looks bad, and the smooth, dusty graphics of the game contrasted with the shiny web 2.0 menus of the site make it worse.
Onto the former. The entire website is consistently gritty and bright, just like the game. They've even paid special attention to the background texture to make the website truly theirs. On a standard sized screen, the first thing you see is the promotions, framed by the logo and 'Buy' incentive image. The menu acts as a navigator to show you where you are, and is cleverly text-based, so that you can browse the site even without images.
Scroll down a bit and you get news, with enough information to give you an idea of whether you want to read it or not.
For the New Horizon website, you have quite a few problems. I suppose it isn't hard now to see that the web graphic design and the art/style of your images is inconsistent.
But even the background image's fade to black is in a completely different style.
The menu needs to go. If I wanted to browse your website, I would click the buttons. I don't need information that I can't even fit on my screen to pop up and cover what I'm currently reading.
There is too much information on the front page, and it's hard to get the most important points. For example, it's even easy to miss the bright orange "Everything you need to play the RPG is available for FREE. Just follow point 1-9 and enjoy the game!"
And have you realised that the text in your facebook widget is dark grey on black? Black backgrounds don't look too great to begin with, but if you want people to actually read the website, do not use white text on a black background. It hurts eyes. Light coloured-text on dark coloured-backgrounds can work but only with a large enough font size and less contrast. For example, I don't mind the white on dark teal that is RMPM.
Also I think I ranted too much. Please don't hate me for having a strong opinion on what I do best :3c <-- Digital Media Degree. Web Maintenance Internship. Volunteer Web Designer.