Could the attacked country invoke Article 5 and compel the other NATO countries to defend it, including by counterattacking the attacking NATO country?
No.
Article 5 states [bold italic emphasis mine]:
if such an armed attack occurs, each of [the Parties] […] will assist the Party or Parties so attacked by taking […] such action as it deems necessary […]
Every Party can decide on their own how to assist the attacked Party or Parties, as it deems necessary. This includes not doing anything at all.
The website you linked to further clarifies [bold italic emphasis mine]:
With the invocation of Article 5, Allies can provide any form of assistance they deem necessary to respond to a situation. This is an individual obligation on each Ally and each Ally is responsible for determining what it deems necessary in the particular circumstances.
and
This assistance is taken forward in concert with other Allies. It is not necessarily military and depends on the material resources of each country. It is therefore left to the judgment of each individual member country to determine how it will contribute.
So,
- Nothing can be compelled, every Party is free to decide on their own.
- Article 5 doesn't say anything about how assistance is to be rendered, it certainly does not mandate a counterattack.
So, any Party can freely choose to counterattack, do something else, or do nothing at all.
When the Treaty was formed, the European Parties very much wanted an automatic military response to be part of the Treaty. In other words, the Europeans wanted the Treaty to be written in such a way that the United States would automatically have to come to their aid. However, the United States didn't want to commit to that, and the wording of Article 5 reflects the United States' wishes of not having to commit to any specific action, or any action at all.