This is a patently wrong statement in an otherwise good article.
There are no known security vulnerabilities with HTTP/1.x's style of compression That's because HTTP/1.x only supports compressing response bodies. During SPDY development, the same compression algorithms used for compressing HTTP responses (gzip/deflate) were applied to compress request and response headers. This is what lead to the CRIME vulnerability. The solution was to still use compression, but use a different compression scheme, HPACK, which (glossing over a ton of technical details) allows compression while avoid CRIME because it "[uses] separate compression dictionaries are used for each source of data." HTTP/2 uses HPACK.
Use of TLS compression is not recommended, but that has always been a performance best practice, since TLS compression is not context aware.
For the love of god, keep using compression with your websites, whether HTTP/1.x, TLS + HTTP/1.x, or HTTP/2