You can't force a private entity to sue another private entity. The regulator (government) can sue it if it finds it at fault. And a private entity can choose to complain to the regulator if it wants. The agreement here between MSFT and GOOG is to try and resolve disputes internally if possible without suing each other or complaining to the regulator. There's nothing illegal in that.
Also the vast majority of contracts these days have "Arbitration clauses" that require all disputes to go through an arbitration process rather than lawsuits in the courtroom.
While there is a great debate to be had that many "Arbitration clauses" far too often curb consumer rights to civil courts (so called "tort reform"; putting limits on what your legal rights are as a consumer), arbitration has "always" been seen as the default first and lawsuits as the necessarily hard next step if arbitration fails (and if a given arbitration clause allows someone their rights to a fair trial in a court of law).
