á ce que

Allison, 

the expressions ‘ attendre que ‘ or s’attendre à ce que … ‘, are needed when there is a relative clause with a different subject, and the subjunctive verb form is then required - somebody awaiting/expecting (that) someone else or something else does something, for example.

It is worth looking closely at the examples in the lesson - they all follow this pattern for attendre que or s’attendre à ce que, although this grammar point could perhaps be reiterated more explicitly in this lesson.

In the example you quote, there is no change of subject - Alain is expecting (himself) to be made redundant/sacked/fired, and ‘ s’attendre à .. ‘ suffices/is correct.

Note also that without a change in subject, the infinitive verb form is used. ( A relevant example for this latter point from the lesson Nous ne nous attendions pas à te voir. )

 If it was the French equivalent of  ‘ Alain is expecting his boss to fire him ‘ , it would require s’attendre à ce que (subjunctive) eg  ‘ Alain s'attend à ce que son patron le licencie. ‘

The link below could be helpful information on the subjunctive conditions, and when the infinitive can be used instead

https://www.lawlessfrench.com/grammar/subjunctive/