Where/when to buy train tickets for Murren -> Interlaken ->Zurich Airport

Why such a big price difference? Am I missing something?

Raileurope is a middle man. Cut out the middle man and the price goes down.

Should I buy the tickets through RailEurope anyway, or perhaps wait and buy tickets for this part of my journey when I arrive in Switzerland. I'm nervous about waiting too long, because I don't want to risk missing my flight from Zurich.

Buy that ticket when you get to Switzerland days before your departure the trains don't sell out
or pay for the convenience and buy it now so you have one less thing to worry about who knows you may lose access to money in the days leading up to your departure from Zurich

You should use https://www.trainline.eu/ instead of Raileurope to buy Interlaken Ost to Zurich airport
It is cheaper by about $55 on the date you want.
Also you could get this route for about 38CHF a super saver fare if you use the sbb site mentioned below. But I think only American Express cards work for online purchases

In Switzerland, you should purchase your ticket through sbb.ch as this is the official site and not a reseller. Unless you are taking a special train, reservations are not required. Think of the majority of trains here like a subway- you buy a ticket and board, take any seat you want.
We have the sbb.ch app on our phones. As we are waiting for the train, we purchase our ticket. There are also ticket machines, ticket agents.

Also, make sure you're comparing apples to apples -- the sbb site assumes everyone has a half-price card, so your price may be double what is listed.

As others have noted, using the railway's own site or trainline.eu is usually cheaper than Rail Europe. Swiss tickets are easy to buy at the station -- I got our Murren-Interlaken-Bern-Lausanne tickets at the Murren station the day before we needed them.

Thanks for the suggestions. I think I will wait and just buy the tickets when I get there, since it sounds like they don't sell out.

Is it worth getting a half-price card or any other Swiss travel card?

We are in Murren for three nights. We will take the cable car to the restaurant high in the mountains that Rick Steves recommends, and have breakfast there ( weather permitting ). Besides that we will probably hike and/or bike around the area.

Since you have spelled out what you plan to do in Murren -> Interlaken ->Zurich Airport. It does not look like you need a pass. It does not look like your train travel will exceed 216 CHF the cost of the Swiss Travel Pass in 2nd class or
the total cost of the Half Price Pass 120 CHF plus all train fares you intend to buy AT HALF PRICE. You have to look up the benefits. Though for certain Swiss Travel Pass covers Schynige Platte.

The Half Fare price from Interlaken Ost to Zurich airport is 37.50 CHF. You don't have a Half Fare card? Then its 75 CHF or about 78 USD. If the total amount of of full fare tickets you plan on buying exceeds 240 CHF, then a Half Fare Card will save you money.

BTW, 47 CHF is the Half fare price for Muerren to Zurich airport.

Thanks for the info. Another leg of my journey involves a train from Vienna to Budapest. If anybody has experience with that, and has an opinion as to whether I should buy the ticket now or when I arrive in Vienna, I'd love to hear. Otherwise I will likely post this in the Vienna section.

You can certainly buy a ticket at www.oebb.at.

For Vienna>Budapest, there IS a substantial reduction for buying ahead. Easy to do on oebb.at. If you check the difference between the price you would pay now for a July trip and the base fare you would pay buying later (or what you would pay to travel today) you can decide whether it's worth it to you.