After updating Jekyll and Kramdown to their latest releases, strikethrough works. Here's an example Morea site illustrating strikethrough:
http://morea-framework.github.io/morea-news-page-example/
The home.md page source is here:
https://raw.githubusercontent.com/morea-framework/morea-news-page-example/master/src/morea/morea/home.md
To make this work correctly I updated gem, jekyll, and kramdown:
% sudo gem update --system
Password:
Updating rubygems-update
Fetching: rubygems-update-2.6.4.gem (100%)
Successfully installed rubygems-update-2.6.4
Parsing documentation for rubygems-update-2.6.4
Installing ri documentation for rubygems-update-2.6.4
Installing darkfish documentation for rubygems-update-2.6.4
Parsing documentation for rubygems-update-2.6.4
Installing RubyGems 2.6.4
RubyGems 2.6.4 installed
Parsing documentation for rubygems-2.6.4
Installing ri documentation for rubygems-2.6.4
% sudo gem update jekyll
Updating installed gems
Updating jekyll
Fetching: jekyll-3.1.6.gem (100%)
Successfully installed jekyll-3.1.6
Parsing documentation for jekyll-3.1.6
Installing ri documentation for jekyll-3.1.6
Installing darkfish documentation for jekyll-3.1.6
Parsing documentation for jekyll-3.1.6
Gems updated: jekyll
% sudo gem update kramdown
Updating installed gems
Updating kramdown
Fetching: kramdown-1.11.1.gem (100%)
Successfully installed kramdown-1.11.1
Parsing documentation for kramdown-1.11.1
Installing ri documentation for kramdown-1.11.1
Installing darkfish documentation for kramdown-1.11.1
Parsing documentation for kramdown-1.11.1
Gems updated: kramdown
Maybe you only need to update kramdown, but this seemed like a good opportunity to update Jekyll as well.