This article displays a rather poor understanding of free speech.

First, it sets up a false dichotomy between an idealized "free speech" past and a present where free speech is in danger. Where's the evidence for this? The US has always had an uneasy relationship with "free speech." I don't believe that the First Amendment was ever interpreted as liberally as this author seems to think.

Any article talking about free speech's decline in the US should refer to the two key Supreme Court cases:
Schenck v. United States and Brandenburg v. Ohio. Seriously, it takes like less than 5 minutes to look these up on wikipedia and you can already see that the First Amendment has always been interpreted pretty conservatively.
Facts are our friends, I wish this author would have provided some citations and historical context.

As for countries other than the US? Are you kidding me? Europe has always had restrictions even on political speech. There's no limiting of free speech that is new here. Sure the author cites some "new" laws but these laws reflect the spirit of the old laws. No news here people.

Now I'll address the author's subcategories where he believe free speech is being eroded:

Blasphemy: This is the only area in the article where the author has a bit of a point. The presence of relatively large populations willing to riot over perceived insults to their religion (i.e. Muslims) is sort of new in Western Europe and leaders are figuring out how to deal with it. However, I don't see anybody rushing out to ban the Satanic Verses. Most leaders are concerned about people doing silly things like dressing up as zombie Muhammed in public. A key criterion here is the possibility of inciting public violence. Rarely do works of literary or artistic merit have this effect, so restrictions are mostly directed towards people doing insulting things in public. Think of going into a bar and insulting the biggest, dumbest looking guy there. Yes, you should have the right to do that, but ask any prosecutor how much sympathy a judge is going to have for your case. There's nothing new here. Personally, I wish our laws allowed more expressions of insulting speech. I actually agree with the author on that point - but the author undermines his case by pretending that we're somehow backsliding. We're not, this has always been the standard.

BTW, I write this as an atheist who plenty of Muslims would love to see butchered. However, we need to remember that much of the censorship going on around this issue is self-censorship. The state censorship he cites is really nothing new - in France it's just an extension of how they deal with Nazis and others. I disagree with French laws on this, but again, there's nothing new here. The author is being alarmist.

Hate crimes
The reason for hate crime laws is that a hate crime is more than just a crime between two people. It's something that has the potential to incite group versus group violence. There's a qualitative difference in an act that's meant to intimidate a a single individual and one meant to intimidate a specific group. When acts directed specifically at a group are committed everyone in that group feels a bit of the effect of the act, hence the punishment should be greater. Additionally, there are some hate criminals who don't mind getting punished just for committing an act against an individual because their real goal is intimidating an entire group.

Speech is discriminatory
Ummm, discrimination on the basis of suspect and quasi-suspect categories has been illegal in many circumstances for some time now. Putting up a sign that says "Coloreds not welcome" at your establishment is pretty much illegal and has been even though it's a restriction on "speech." This is based on the fact that you're operating a public establishment and therefore derive gains from being part of the broader society. With those gains come responsibilities. If you and your buddies don't want to hang around blacks when you BBQ in your backyard you're still free to discriminate because you're not running a public establishment in that context. The example cited in the article comes from a comedy club, a public establishment. Again, nothing new here.

Speech is Deceitful
If you lie and get a benefit from it, then yes, you should be prosecuted. I don't know why the author views this as a problem. The example he cites from France is not an outlier in French history - it's an extension of France's rather stringent anti-hate laws. Laws I disagree with just like the author does, but again, there's nothing new here.

One of the reasons I really don't like this article is because I kind of agree with the author around loosening free speech standards, but he just does an awful and alarmist job of conveying his point. He is bound to turn off anyone who has any grasp of the history and nuance around the subject. I feel like a cause I support has been set back by this author's very poor argumentation skills.

This article reminds us that opinion column writers were the original trolls long before the Internet ever existed.

tl:dr: The author does not provide any convincing evidence that the "West is limiting Free Speech" in any new way.