What does it mean when addresses are labelled "beyond the gap limit (highlighted red)"?
If you have your wallet seed it is fine:
From what I understand, your coins are safe, they will not be lost as long as you have wallet seed. When reimporting, Electrum would just not look far enough to find everything, until you nudge it a bit.

Explanation:
The gap limit gives the number of addresses that Electrum will generate from the seed starting from the last address that it found a balance on.

The error message tells you that Electrum wouldn't find some of your addresses by itself, because Electrum would think that it arrived at the end of your transaction history, before all your transaction history is discovered.

Example to make it graphic: 


Gap limit = 3
S is Seed
I address with balance
• address without balance.
X address with balance beyond gap-limit


An arbitrary transaction history:
You have a balance on a few addresses, already spent/didn't use some addresses intermittently, and then you skipped a bunch (five here) for some reason before receiving balances on some more.

SIIII•III••I•III•I•IIII•••••XXX
                       ^gap^


The gap of five is bigger than the currently set gap limit of three, so now, reimporting the seed, Electrum would only regenerate to:

SIIII•III••I•III•I•IIII•••
    last used address ^ +3


Because it will only regenerate gap-limit unused addresses after an address with a balance.

If you set the gap limit higher (in the example to six), or use the previously unused addresses that make up the gap, Electrum will rediscover the addresses.

The imported wallet so far:

SIIII•III••I•III•I•IIII•••


Receive 4 new transactions N:

SIIII•III••I•III•I•IIIINNNN••XXX
                             ^ oh, that "new address" was used!


Recovery of all addresses with balances plus gap-limit new addresses:

SIIII•III••I•III•I•IIIIIIII••III•••


Altogether, it shouldn't be much of a problem. Electrum should probably be able to safely store thousands of addresses, so unless you created a humongous gap, probably no need to think about any problems there.

So, what you might want to do, is figure out just how many addresses you have now generated from your wallet seed. If you then want to recover your wallet on another computer, just generate the same amount of addresses or temporarily increase the gap limit until you have the same number of addresses.