End users can't force the spellchecker for the file types that are provided by the third-party plug-ins. Plugin maintainer needs to support it explicitly.
For example, Java plug-in defines this in the plugin.xml
descriptor:
<spellchecker.support language="JAVA" implementationClass="com.intellij.spellchecker.JavaSpellcheckingStrategy"/>
Plugins can also provide their own dictionaries:
<extensions defaultExtensionNs="com.intellij.spellchecker">
<support language="Python" implementationClass="com.jetbrains.python.spellchecker.PythonSpellcheckerStrategy"/>
<bundledDictionaryProvider implementation="com.jetbrains.python.spellchecker.PythonBundledDictionaryProvider"/>
</extensions>
SpellcheckingStrategy class specifies how the words in the file type are tokenized and supplied to the spellchecker.
For open source plug-ins like Markdown, you can try to support it yourself and then send pull request or patch to the maintainer, or just kindly ask the maintainer to add spellchecker support in the future updates.