You selected Engelberg as the destination. This is the train station in the village of Engelberg, at the foot of Mt. Titlis, and not the summit station. To buy a ticket to the summit station, choose “Engelberg, Klein Titlis, Kleintitlis”.
The 19.80 you mention is a Supersaver ticket to Engelberg. You must stick to that itinerary, otherwise your ticket is not valid. If you miss the train because you were late at the station, you have to buy a new ticket. If you want a fully flexible ticket, valid on any train, for any connection, you need a Point-to-Point ticket which is CHF 61, one way, with the Half Fare Card, see my example:
Mt. Titlis is quite a costly mountain trip, one of the most expensive in our country, even for holders of the Swiss Half Fare Card. I therefore strongly suggest not buying tickets in advance but on-site, once the weather forecast is reliable, this isn’t the case for more than 2 days out.
Please let me know if I can assist you any further.